Fields Flashcards
(148 cards)
1
Q
What is a field?
A
A region in which a body experiences a non-contact force.
A field arises from the interaction of mass, of static
charge, and between moving charges.
2
Q
What is gravity?
A
A universal attractive force acting between all matter.
3
Q
What is Newton’s Law of attraction?
A
Every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
4
Q
What is the equation for force between point masses?
A
F = Gm(1)m(2)/r²
G is the ‘universal gravitational constant’
Every massive object in the universe attracts every other massive object. The force is always attractive.
5
Q
What is a gravitational field?
A
The Earth applies a force to everything within its gravitational field.
The field due to a body is the region of space surrounding it where other bodies will feel a force due to it.
Gravitational fields have infinite reach.
6
Q
What is a radial field?
A
The field lines become more spread out as the distance from a spherical object increases, increasing the diminishing strength of the field.
The force per unit mass varies inversely with distance squared.
NB: The field is 3D.
The gravitational field is radial in the region surrounding the Earth i.e. for satellites.
7
Q
What is a uniform field?
A
The field lines are parallel and equidistant, indicating that the field is constant.
The gravitational field is uniform close to the Earth’s surface i.e. for cars, balls, planes, etc.
8
Q
What are the rules about field lines?
A
- They don’t start and stop in empty space. They end on a mass and extend back all the way to infinity.
- They never cross.
9
Q
What is gravitational field strength?
A
Your pull on the earth = the earth’s pull on you. But your gravitational field is far weaker.
The field strength at a point in a body’s field is the gravitational force exerted on an object placed at that point, per kg of the object’s mass.
i.e. the no of newtons of attractive force acting per kg of the object’s mass
g = F/m
The gravitational field strength at a point in a field does not depend on the mass placed there - it is a property of the field.
Therefore, two objects of different mass placed at the same point in the field will experience the same field strength, but a different force.
10
Q
What is the difference between a and g?
A
They have the same symbol but a different unit.
11
Q
What is the gravitational field strength in a radial field?
A
g = F/m but F = GMm/r²
therefore, g = GM/r²
12
Q
What is gravitational potential?
A
The gravitational potential at a point in a gravitational field is the work done in moving a unit mass from infinity to that point.
OR
The gravitational potential at a point in a field is the energy per unit mass.
V = Ep/m
It has a 0 value at infinity.
NB: The answer for V is the same for everyone at the same point in the field.
13
Q
What is gravitational potential difference?
A
If a mass is moved from one position to another, there is a change in gravitational potential.
Therefore, there is also a change in gravitational potential energy.
This is the work done in moving a mass.
ΔEp = mΔV
The actual value is always higher as frictional forces have to be overcome i.e. drag force within the Earth’s atmosphere.
14
Q
What is an equipotential surface?
A
All points on an equipotential surface have the same gravitational potential.
The lines are always perpendicular to the gravitational field.
Due to this, the gravitational potential difference is zero when moving along the surface, so no work is done when moving along an equipotential surface.
15
Q
What is gravitational potential energy?
A
The energy an object possesses because of its position in a gravitational field.
In a uniform field, Ep = mgh
In a radial field, Ep = - GMm/r = GM(E)m(1/r(2) - 1/r(1))
The energy doesn’t vary as rapidly.
16
Q
What is gravitational potential in different fields?
A
In uniform:
V = Ep/m but Ep = mgh therefore V = gh
In radial:
V = Ep/m but Ep = -GMm/r therefore V = -GM/r
17
Q
Why is gravitational potential negative?
A
Positive work must be done against gravity (by an external force) to move an object away from the Earth. The object gains potential energy if moved away from the Earth.
But it has zero potential energy at infinity.
Hence it must have negative potential energy when closer to Earth than infinity.
18
Q
What two graphs can be drawn?
A
g against r
V against r
19
Q
How is g related to V?
A
V = -GM/r
but g = GM/r²
therefore g = -ΔV/Δr
This is the gradient of the V-r graph.
20
Q
How can a g-r graph be used?
A
Area: ΔV
Area x Mass: Work Done
21
Q
How can a mg-r graph be used?
A
Area: Gravitational Potential Energy
22
Q
What are Kepler’s Laws?
A
- The orbit of every planet is an elipse with the Sun at one focus.
- A line joining the planet to the Sun sweeps out equal areas in equal times.
- The time for one orbit, T and the average distance from the planet to the Sun, r are related by T² ∝ r³.
23
Q
What was Newton’s proof?
A
Assuming the orbit of a planet is circular, there must be a RF towards the center of the circle i.e. a centripetal force.
This is provided by the gravitational attractive force of the Sun.
F = mv²/r and F = GMm/r²
therefore, mv²/r = GMm/r² so v²r = GM
but v = 2πr/T so 4π²r³/T² = GM
therefore, T²/r³ = 4π²/GM (everything is constant)
24
Q
Why are equipotential surfaces useful for satellites?
A
A satellite orbiting the Earth along an equipotential line does 0 work as ΔV = 0 and the force is always at 90°. Therefore, Ek isn’t lost, else the satellite would fall towards the Earth.
25
What is the total energy for an orbiting satellite?
The total energy of an orbiting satellite is made up of its kinetic and potential energy, and is
constant.
For example, if the height of a satellite is decreased, its gravitational potential energy will
decrease, however it will travel at a higher speed meaning kinetic energy increases, therefore total
energy is always kept constant.
total energy = Ek + Ep
If speed = constant, there is no gain in Ek. All of the GPE is converted to heat energy in the brakes - there is a risk of break failure.
26
What is escape velocity?
```
Ep = -GMm/r and Ek = 0.5mv²
Ep + Ek = 0 (energy is conserved)
-GMm/r + 0.5mv² = 0
Therefore, v = √2GM/r
g = GM/r² so gr = GM/r
Therefore, v = √2gr
```
27
What is a synchronous orbit?
The orbital period of the satellite is equal to the rotational period of the object that it is orbiting.
For example a synchronous satellite orbiting Earth would have an orbital period of 24 hours.
28
What are geostationary satellites?
- These satellites follow a specific geosynchronous orbit, meaning their orbital period is 24 hours and they always stay above the same point on the Earth, because they orbit directly above the equator.
- They are very useful for sending TV and telephone signals because it is always above the same point on the Earth so you don’t have to alter the plane of an aerial or transmitter.
29
How is the orbital radius of a geostationary satellite calculated?
r³ = GMT²/4π²
r³ = = 6.67×10 ×5.97×10 ×(24×60×60)² / 4π²
therefore, r = 4.22 x 10^7m
30
What are low orbit satellites?
-These satellites have significantly lower orbits in comparison to geostationary satellites (r<200km), therefore they travel much faster meaning their orbital periods are much smaller.
-They travel over large sections of the Earth in short time periods.
-Because of this, these satellites require less powerful transmitters and can potentially orbit across the entire
Earth’s surface, this makes them useful for monitoring the weather, making scientific observations about places which are unreachable and military applications.
-They can also be used for communications but because they travel so quickly, many satellites must work together to allow constant coverage for a certain region.
31
How can the null point be calculated?
At null point, resultant g force = 0.
GM/x² = GM/(r-x)²
therefore x²/(r-x)² = M/M
32
How is g related to ρ?
g ∝ ρr
33
What is charging up?
Charge can transfer between two objects when they slide past each other.
Electrons leave one surface and join the other.
-The object losing electrons has a positive charge.
-The object gaining electrons has a negative charge.
Electrons will move to or from the Earth to balance the charges on the object (earthing).
If one of the objects is an insulator, charge can build up.
34
What happens in a Van de Graaf generator?
The dome is metal.
| Therefore, charge builds up because it is isolated.
35
What happens to rods?
- If two rods of the same charge are brought together, they repel.
- If two rods of opposite charges are brought together, they attract.
- If a rod is brought near an uncharged object, they attract.
36
Why does the effect change with distance?
The electric field around the rod is stronger when it is closer.
37
How do we charge up a gold leaf electroscope?
- Bring a charged object near the electroscope.
- Earth the electroscope.
- Take the charged object away.
38
What is an electric field?
A charged object sets up an electric field around itself. Any other charged body which comes into the field will experience a force:
-Like charges repel
-Unlike charges attract
The electric field is strongest near the charged object, and gets weaker as you move further away.
39
What are field lines?
They represent electric fields and show the direction of the force which would be felt by a small positive charge.
The field is strongest where the lines are closest together
Equally spaced lines show a uniform field.
40
What are the rules for field lines?
- They never start or stop in empty space - they start or stop at a charge or 'at infinity'.
- They never cross - if they did, a small + charge would feel forces in different directions, which could be resolved into one true direction of the field line there.
- The density of the field lines on a diagram is indicative of strength of the field.
- There is a neutral point, exactly between two like charges, where no field exists. This is because the forces on a charge placed there would be exactly equal and opposite)
41
What are some examples of electric field patterns?
- Electric field from an isolated positive charge.
- Electric field from an isolated negative charge.
- Oppositely charged points (+ to -).
- A point near a plate.
- Oppositely charged plates (+ to -).
42
How can an electric field be visualised?
Using electrolytic tanks and conducting paper.
Equipment:
Damp (salt solution) filter paper
Potassium permanganate crystals
250V electrodes
Method:
-Plot equipotential lines using a point probe attached to a voltmeter.
-Field lines plotted perpendicular to equipotential lines.
43
What is Coulomb's Law?
The force between two point charges is:
-Directly proportional to each of the charges Q1 and Q2.
-Inversely proportional to the square of their separation.
F = kQ1Q2/r²
NB: For a charged sphere, the charge may be considered to be at the centre.
44
What is k?
k depends on the pemittivity (ε) of the substance separating the charhes.
k = 1/4πε
45
What is ε?
This is the capability of the material to permit electric field lines.
Air can be treated as a vacuum when calculating the force between charges.
Therefore, the permittivity of free space is used, ε0.
Every insulating material has a permittivity greater than ε0.
46
What is the permittivity of water?
The permittivity of water is about 80x the permittivity of free space.
This makes the force between the charges 1/80th of the value.
Salt crystalline structure is provided by the forces of attraction between + sodium ions and - chloride ions.
When salt is put in water, the forces are reduced and the crystal structure collapses.
47
What is electric field strength?
The force per unit charge exerted by the field.
E = F/Q
NB: Q is not the source of the electric field.
48
What is electric field strength in a uniform field?
E = V/d
49
How is this derived?
```
Work done moving an object:
W = Fd
Work done when charge moves through a pd:
ΔW = QΔV
therefore, Fd = QΔV
F/Q = V/d
```
50
How can the strength of a uniform field between parallel plates be increased?
- Increasing the p.d. across the plates.
| - Decreasing the distance between the plates.
51
What are electron beams?
-TVs, oscilloscopes, computer monitors and X-ray machines all produce fast-moving electrons.
-They use an electron gun to produce electrons by thermionic emission.
-The electrons are then accelerated by an electric field. As the electrons accelerate across the field (cathode to anode), they lose Ep but gain Ek.
-For electrons of mass m and charge e moving through a pd V:
gain in Ek = loss in electric potential energy
0.5mv² = eV
52
What is electron deflection?
Twice the moving electrons move through an electric field between two plates.
The plates are d apart and have pd V across.
Electric field strength: E = V/d
Force of e- charge: F=eE
therefore, F = eV/d
This force is constant and so the electrons travel in a curved path.
RECALL DIAGRAM
53
How can velocity be calculated?
Ek = 0.5mv²
E = eV
EQUATE!
or SUVAT
54
How can acceleration be calculated?
a = F/m where F = eV/d
55
What is electric field strength in a radial field?
E = F/Q but F = kQ1Q2/r²
therefore, E=kQ/r²
NB: Q is the source of the electric field.
56
What is F if the particle is stationary?
F = mg
57
How to calculate charge on e-?
```
vol = 4πr³/3
mass = density x vol
weight = mg
E = F/Q therefore F = EQ
but F = mg, therefore EQ = mg
E = V/d therefore, Q = mg/E
```
58
What is electric potential?
All points in an electric field have an absolute electric potential, V.
This is the electric potential energy that a unit positive charge would have at that point in an electric field.
V = kQ/r
The sign of V depends on the sign of Q.
V is +ve when Q is +ve and the force is repulsive.
V is 0 when r is ∞.
NB: Q is the source of the electric field.
59
What do the graphs of V-r look like?
-V-r for a positive charge is a negative correlation.
-V-r for a negative charge is a positive correlation.
RECALL
60
How can a V-r graph be used?
The gradient of a tangent gives the field strength at that point.
E = ΔV/Δr
61
What is electric potential difference?
If two points in an electric field have a different absolute electric potential, then there is an electric potential difference between them.
This is the energy required to move a unit charge between two points in an electric field that have a different absolute electric potential.
62
How can an E-r graph be used?
The area is ΔV i.e. electric potential difference.
63
How can work done be calculated?
The work done in moving charge Q is given by:
AKA electric potential energy.
ΔW = QΔV
-If an e- is in the electric field of a +ve charge, there is a force of attraction.
-The e- electric potential energy is converted to kinetic energy as the electric field moves the e- closer to the point charge. The electric field does work on the e-.
-The e- kinetic energy is converted to electric potential energy as the electric field moves the e- further from the point charge. Work is performed against the electric field.
-If the e- is moved along the arc of a circle with a constant radius, 0 work is done. This is because ΔV=0 because r remains constant.
64
What is an equipotential?
Equipotential lines are perpendicular to field lines.
| No work is done when you travel along an equipotential line which means that no energy is transferred.
65
What size of charge on a third point placed midway between two points, would result in the doubling of the magnitude of the force on one of the initial charges?
2F = F + kQ1Q3/(r/2)²
66
What is the electric potential at a point midway between two charges that are equal and opposite?
0
67
How do electrons react to a positive charge?
The electron beam forms a circular trajectory around the charge, as the electrons experience a centripetal force of attraction.
The centripetal force is always perpendicular to the velocity of each electron, therefore no work is done on the e-.
Thus, the kinetic energy and speed of the particles remain constant but the direction of motion is affected.
68
How is velocity calculated in circular motion?
mv²/r = kQ1Q2/r²
| REARRANGE!
69
Gravitational Fields v Electric Fields?
Feels the force:
- mass, m
- charge, q
Definition:
- Force per unit mass.
- Force per unit charge.
Constant of proportionality:
- G, the universal gravitational constant
- k, where ε = permittivity of the medium
Relationship with r:
- Inversely proportional to r²
- Inversely proportional to r²
Force equation:
- F = mg
- F = EQ
Direction of force:
- All masses attract
- Like charges repel and unlike charges attract
Relative strength:
- Weak, accept for massive bodies - responsible for the motion of planets
- Strong at close range - responsible for chemical bonding
70
What is the difference in magnitude of gravitational and electrostatic forces between subatomic particles?
The magnitude of electrostatic forces between subatomic particles is much greater than the magnitude of gravitational forces.
This is because the masses of subatomic particles
are incredibly small whereas their charges are much larger.
71
What is a capacitor?
Capacitors store electric charge.
They are used in almost all electric circuits.
A capacitor consists of two parallel metal plates separated by an insulator called a dielectric.
The more charge a capacitor can store, the greater its capacitance, C.
Capacitors have a working voltage marked on them which must not be exceeded.
72
What is capacitance?
The capacitance of a capacitor is the charge stored per unit of potential difference across it.
Q = CV
73
What is a farad?
The unit of capacitance is the farad: 1CV-1.
A farad is a very large unit. Values are usually marked in picofarads or microfarads.
1pF = 1x10^-12F
74
What are the factors affecting the capacitance of a parallel plate capacitor?
C = Aε0εr/d
where:
A = cross-sectional area of overlap of plates
ε0 = permittivity of free space (Fm-1)
εr = relative permittivity of the dielectric
d = distance between the plates
75
What is relative permittivity?
- The dielectric constant of the material.
- εr is calculated from εm/ε0 where εm is the permittivity of the material used as the dielectric.
- It has no unit.
76
What is the action of a dielectric?
A dielectric material is an electrical insulator that can be polarised by an applied electric field.
When a dielectric is placed in an electric field, electric charges do not flow through the material as in a conductor, but only slightly shift from their equilibrium positions causing dielectric polarisation.
RECALL DIAGRAM.
77
What is dielectric polarisation?
Due to dielectric polarisation, +ve charges are displaced towards the field and -ve charges shift in the opposite direction.
This creates an internal electric field that reduces the overall field within the dielectric itself, so reducing the p.d. across the capacitor.
To return the p.d. to its original value requires the addition of more charge onto the plates.
Therefore, the capacitor can store more charge for the same p.d. and increase its capacitance.
78
What is the energy of a capacitor like?
Capacitors only store small amounts of electric charge.
To store the same energy as an AA cell, they would need to be about 6000F.
Capacitors are used to provide power for a short amount of time.
They can discharge all of their charge in a fraction of a second so charged capacitors can be dangerous.
79
How is energy stored in the capacitor?
When a capacitor is charged, you push electrons onto one plate and off the other.
The power supply does work on the e- so their potential energy increases.
This energy is stored in the electric field between the plates.
80
How can a Q-V graph be used?
The energy stored is the sum of all the energies stored in each small increase of charge. So the energy is the area under the graph.
E = 0.5QV
as Q = CV
E = 0.5CV² OR E = 0.5Q²/C
81
What happens in the charging circuit of a capacitor?
Electrons flow from the -ve terminal of the power supply to one plate of the capacitor and from the other plate to the +ve terminal of the power supply.
When the switch is close, and charging starts, the rate of flow of charge is large (i.e. a big current) and this decreases as time goes by and the plates become more charged so 'resisting' any further charging.
82
How does a resistor affect the circuit?
The addition of a resistor in the circuit in series with the capacitor only affects the time it takes for the capacitor to become fully charges and not the eventual p.d. across it.
The p.d. is always the same and equal to the p.d. across the supply.
The p.d. is only shared when the charges are flowing.
As charge builds up on the plate, the p.d. across the resistor diminishes as the charge, Q = 0 (across resistor).
83
What do the graphs look like for a charging circuit?
- V-t is half a rainbow.
- Q-t is half a rainbow.
- I-t is an upside down half rainbow.
84
How can a Q-t graph be used?
The gradient of the tangent to the curve at a point gives the current at that time.
85
How can an I-t graph be used?
The area between the curve and the time axis gives the charge stored.
86
What are the equations for a charging circuit?
V=V0(1-e^-t/RC)
Q=Q0(1-e^-t/RC)
I=I0e^-t/RC
87
What is the time constant?
When t = RC
This is the time taken for the p.d. across the capacitor and the charge on the capacitor to get up to (1-1/e) of its max values and the time taken for the discharging current to drop to 1/e of its original value.
To find RC, find the time where the values are 0.67 of max value (for V or Q) or the time where the value is 0.37 of max value (for I).
88
What is the half life?
T1/2 is the time for the charging current to halve.
T1/2 = 0.69RC
DERIVE THIS!
89
What happens in the discharging circuit of a capacitor?
As soon as the switch is closed, a large current starts to flow and the p.d. across the capacitor drops.
As charge flows from one plate to the other through the resistor, the charge is neutralised and so the current falls and the rate of decrease of p.d. also falls.
90
What is discharge theory?
Eventually, the charge on the plates is 0 and the current and p.d. are also 0 - the capacitor is fully discharges.
Note: The value of the resistor does not affect the final p.d. across the capacitor, only the time that it takes to reach that value.
The bigger the resistor, the longer the time taken to discharge.
91
What do the graphs look like for a discharging circuit?
- V-t is an upside down half rainbow.
- Q-t is an upside down half rainbow.
- I-t is an upside down half rainbow.
92
How can a Q-t graph be used?
The gradient of the tangent to the curve is equal to the current at that point in time.
93
How can an I-t graph be used?
The area between the curve and time axis is equal to the charge that has flowed.
94
What are the equations for a discharging circuit?
V=V0e^-t/RC
Q=Q0e^-t/RC
I=I0e^-t/RC
95
What is the time constant?
When t = RC
This is the time taken for the discharging current, the p.d. across the capacitor and the charge on the capacitor to drop to 1/e of their original values.
To find RC, find the time where the values are 0.37 of max value (for V, Q or I).
OR use log graph!
96
What is the half life?
T1/2 is the time for the discharging current, the p.d. across the capacitor and the charge stored on the capacitor to halve.
T1/2 = 0.69RC
DERIVE THIS!
97
Explain the log graphs ...
```
e.g. for V
V=V0e^-t/RC
lnV = lnV0 + lne^-t/RC
lnV = lnV0 - t/RC
therefore y = mx + c
therefore m = -1/RC
The log graphs of V, Q and I all have this gradient.
```
98
What are the uses of a capacitor?
-In a camera flash
-In a backup power supply
-To smooth dc power supplies
-To monitor breathing patterns in babies
RECALL GRAPH
99
How is a capacitor used in a camera flash?
Even a large capacitor stores only a small amount of energy, but it can release this energy very rapidly - as in a flash gun.
The charged capacitor in a flash gun discharges and releases around 1J of energy in 2ms. This is a power output of 1kW.
The small camera battery cannot produce this power output. Therefore, it takes 10 seconds for the battery to recharge the capacitor between photos.
100
How is a capacitor used to monitor breathing patterns in babies?
The sensor consists of a sealed sachet filled with a sponge.
As the baby breaths the sachet compresses and expands and the pressure of the air in the sponge varies.
The sealed tube transfers this pressure variation to the detector and the flexible capacitor plates move up and down.
This changes the separation of the capacitor plates and therefore the capacitance of the detector.
Charge flows on and off the plates as the capacitance changes. producing an electrical signal which is then monitored.
101
What are some examples of capacitors?
A is made large and d is made small.
- A waxed paper capacitor consists of two long strips of metal foil separated by strips of waxed paper. It is rolled up to form a cylinder. The typical value is 0.1μF.
- An electrolytic capacitor has a similar 'Swiss Roll' construction. Its very thin dielectric is formed chemically. The plate marked + must never be charged negatively. The typical value is 100μF.
- The mica capacitor consists of layers of metal foil separated by thin sheets of mica. The typical value is 0.01μF, but they have high stability - they keep their value with age.
102
What is the 'maximum working voltage' of a capacitor?
If the p.d. across the plates is made too high, the electric field between the plates will cause the dielectric to 'break down'. One the dielectric conducts, the capacitor cannot store charge.
103
What do magnetic fields look like?
RECALL DIAGRAMS
The field lines always go from North to South.
-One magnet.
-Two magnets of opposite polarity.
-Two magnets of the same polarity (neutral point).
-Straight current-carrying conductor.
-Current carrying coil (inside coil, lines go S-N).
104
What happens to a current-carrying wire in a magnetic field?
A current-carrying wire in a magnetic field experiences a force when the field is perpendicular to the current.
The direction of the force can be worked out using Fleming's left hand rule.
F = BIL
The magnitude of the force can be increased by:
-Increasing the strength of the magnetic field.
-Increasing the magnitude of the current flowing through the wire.
-Increasing the length of the wire within the magnetic field.
105
What is magnetic flux density?
The magnetic flux density, B of a magnetic field, is a measure of the strength of the field, and it is measured in the unit Tesla.
NB: Calculate significance of Earth's magnetic flux density by B(earth)/B(field) x 100.
106
What is the Tesla?
A force of 1 N on 1m of wire carrying 1A of current perpendicular to a magnetic field.
1T = 1N/Am
107
What happens to a charged particle in a magnetic field?
A charged particle, moving through a magnetic field, experiences a force when the field is perpendicular to the velocity.
The direction of the force can be worked out using Fleming's left hand rule.
F = BQv
The magnitude of the force can be increased by:
-Increasing the strength of the magnetic field.
-Increasing the magnitude of the charge on the particle.
-Increasing the velocity of the particle.
The force = 0 if:
-The charged particle is at rest, as v = 0.
-The charged particle moves parallel to the magnetic field, as vsinθ = 0 if θ = 0.
NB: This is why a force is exerted on a current-carrying wire, because it contains moving electrons, which are negatively charged particles.
108
How does the charge on the particle affect the direction of the force?
+ve:
Use Fleming’s left hand rule, using the second finger as the direction of travel.
-ve:
Use Fleming’s left hand rule, but reverse the direction of your second finger.
This is because the seCond finger represents Conventional Current, which flows from positive to negative i.e. opposite to the direction of the flow of -ve charge.
109
How are magnetic field lines affected by current?
-If the current is reversed, the field lines point in the opposite direction.
If the current is increased in magnitude, the field lines move closer together.
110
Why do charged particles move in circular paths?
When a charged particle moves at right angles to a magnetic field, the constant force (F = BQv) is perpendicular to both velocity and the field.
Therefore, it continuously changes the particle's direction of motion and has no effect on its speed.
The result is that the charged particle moves in a circular path.
An object can only move in a circular path if a centripetal force acts on it.
BQv = mv²/r
Therefore, the radius of the circular path of the charged particle:
r = mv/BQ
r ∝ mv as BQ = constant
111
What is the time period for an e- to make one rotation?
T = 2πr/v but r = mv/BQ
therefore T = 2πm/BQ
r cancels, and time doesn't depend on r
In a magnetic field of constant flux density, the time period of the electron does not depend on its speed.
A faster moving electron moves in a circle of a larger radius, but takes exactly the same time to make one revolution.
NB: If semi-circle, only πr/v.
112
What is a cyclotron?
A particle accelerator which uses the circular deflection of charged particles in a magnetic field.
It is used in hospitals to produce high-energy beams for radiation therapy.
It is formed of two semi-circular electrodes called 'Dees' in a vacuum chamber, with a uniform magnetic field acting perpendicular to the plane of the electrodes, and a high frequency alternating voltage applied between the electrodes.
The charged particles move from the centre of one of the electrodes, and are deflected in a circular path by the magnetic field.
NB: The force exerted by the magnetic field is always perpendicular to the direction of travel, so the particle’s speed will not increase due to the magnetic field, which is why there is an alternating electric field between the electrodes.
Once the particles reach the edge of the electrode they begin to move across the gap between the electrodes, where they are accelerated by the electric field, meaning the radius of their circular path will increase as they move through the second electrode.
When the particles reach the gap again, the alternating electric field changes direction allowing the particles to be accelerated again. This process repeats several times until the required speed is reached by the particles and they exit the cyclotron.
113
What is magnetic flux?
If a uniform magnetic field of strength B acts perpendicular to an area A, the magnetic flux Φ is given by:
Φ = BA
1 Wb = 1Tm²
If the plane of the area is not perpendicular to the field, but is inclined at some angle θ, then:
Φ = BAcosθ
114
What is flux linkage?
For a coil with N turns cutting the flux, the magnetic flux linking the coil, the flux linkage is given by:
flux linkage = NΦ
If the rectangular coil is rotated in the magnetic field, then:
Φ = BAcosθ
therefore NΦ = BANcosθ
115
What is electromagnetic induction?
When a conducting rod moves relative to a magnetic field, the electrons in the rod will experience a force (as they are charged particles), and build up on one side of the rod, causing an emf to be induced in the rod.
This phenomenon also occurs if you move a bar magnet relative to a coil of wire, and if the coil forms a complete circuit, a current is also induced.
This is because the magnetic flux linkage through the coil is changed as the lines of magnetic flux are cutting the coil, thus producing a voltage - the induced emf.
116
What is Faraday's Law?
The magnitude of the induced emf is equal to the rate of change of flux linkage.
induced emf = change in flux linkage/time taken
E = ΔNΦ/Δt
117
What is Lenz's Law?
The direction of induced emf is such that it will try to oppose the change in flux that is producing it.
Therefore, E = -ΔNΦ/Δt
The minus sign reminds us that the emf is always induced in a direction so as to oppose the change in flux.
118
What is the emf of a straight conductor moving in a magnetic field?
s = vΔt
if distance travelled = width, then A =lvΔt
therefore, ΔΦ = BA = BlvΔt
but E = ΔΦ/Δt, therefore E = Blv
This is the magnitude of emf induced by a straight conductor of length l, moving in a magnetic field of flux density B.
119
What is the derivation of the emf equation?
V = W/Q = BILΔS/IΔt = BLΔS/Δt
| but LΔS = A therefore emf = BA/Δt
120
Why is no emf induced if a magnet is entirely inside a coil?
ΔB is constant so there is no change in the magnetic flux density.
Therefore, the emf = 0.
121
What does a negative section of a trace of the emf induced in a coil as a magnet accelerates through mean?
The trace is -ve, as by Lenz's Law, emf is always induced so as to oppose the change in flux.
Therefore, when the magnet comes out of the coil, the emf is induced in the opposite direction.
The peak emf is greater over this section as the magnet is moving faster because of its acceleration due to gravity. Therefore, there's a smaller Δt for the same ΔB, hence the emf is higher in magnitude.
The greater speed of the magnet also results in a shorter time interval.
122
What is a simple A.C. generator?
A generator converts kinetic energy into electrical energy.
Each end of the coil is connected to a slip-ring, which rotate with the coil and press against stationary carbon brushes.
Each side of the coil always makes contact with the same brush.
As the coil rotates as a steady rate, the flux linkage of the coil constantly changes.
Therefore, an emf is induced. It is alternating, meaning it changes direction with time.
123
What does the graph for a generator look like?
The graph shows how the induced emf changes as the coil rotates once in the magnetic field.
It is a cos graph.
One complete revolution of the coil gives one cycle of A.C.
124
How can the peak emf be increased?
This is achieved by increased the rate of change of flux linkage of the coil as it spins by:
- Using a coil with more turns
- Using a coil with a larger cross-sectional area
- Increasing the strength of the magnetic field
- Increasing the frequency of rotation of the coil
125
How does frequency of rotation affect the graph?
The frequency of rotation will also affect the frequency of the A.C. signal.
The quantities are proportional - doubling the speed, will double the emf and double the frequency.
126
What is the equation for induced emf of a coil rotating at constant frequency in a magnetic field?
- flux linkage = BANcosθ
- but when a coil rotates at a constant frequency in a magnetic field, how fast θ changes depends on the angular speed, w of the coil
- therefore, flux linkage = BANcoswt
- but induced emf = rate of change of flux linkage, therefore this is the derivative of the formula for magnetic flux linkage with respect to time
- therefore, E = BANwsinwt
- the max change happens when θ = 90, so it varies sinusoidally
- the emf is greatest when sinwt = ±1
127
When is the magnitude of emf at a max?
At θ = 90 and sinwt = ±1.
At this point, the value for the flux linkage of the coil = 0.
induced emf = change in flux linkage/time
The change in flux is greatest when the plane of the coil is parallel to the magnetic field because the coil cuts the magnetic field lines perpendicularly.
128
What is an oscilloscope?
Any type of current can be displayed on an oscilloscope, which shows the variation of voltage with time.
If the time-base is switched off, the trace shows all the possible voltages at any time in one area - this is useful for taking measurements.
129
What do DC traces look like?
e.g. if a battery or cell is connected to an oscilloscope
The current of the DC supply is constant, so the voltage is constant.
If the battery or cell is reversed, the current and voltage are constant in the other direction.
The trace will show a straight line parallel to the x-axis, at the height of the output voltage.
This line can be +ve or -ve.
If the time-base is switched off, a dot is seen on the screen at the height of the output voltage.
130
What do AC traces look like?
e.g. if anything that draws power from the Mains Supply is connected to an oscilloscope
The current is constantly changing from maximum flow in one direction to maximum flow in the other direction, and the voltage is doing the same.
The trace will show a repeating sinusoidal waveform.
If the time-base is switched off, a straight vertical line is seen on the screen, showing all the possible output voltages.
131
What are the controls of an oscilloscope?
An oscilloscope has a fixed grid on its display, but the scale of both axes can be adjusted to make measurements easier.
To display a direct current, connect a DC power supply into the Y-input of the oscilloscope.
To display an alternating waveform, connect an AC power supply into the Y-input of the oscilloscope.
The Y-gain control dial allows adjustment of the volts/division. This changes the value of each vertical square.
The time base dial allows adjustment of the scale of the X-axis. This changes the value of each horizontal square.
132
How are measurements taken from an oscilloscope?
Voltage:
To measure the voltage of a DC supply, count the number of vertical squares from the origin to the line, and multiply by the volts/div.
To measure the peak voltage of an AC supply, count the vertical squares from the centre of the wave to the top, and multiply by the volts/div.
Time and Frequency:
To measure T for one wave, count the number of horizontal squares in one wavelength, and multiply by the time base.
f = 1/T
133
What is the peak value?
The max value of I or V in either direction.
It is the amplitude of the wave i.e. distance from equilibrium to highest or lowest point.
They are denoted as I0 or V0.
134
What is the peak-to-peak value?
The range of values of I or V.
| This is the distance from the minimum point to the maximum point.
135
What is time period?
In an AC current or voltage, this is the time taken for one complete cycle.
This is the distance from one point on a curve e.g its peak, to the point where the curve repeats, e.g, the next peak.
136
What is frequency?
The number of complete cycles that occur per second.
| f = 1/T
137
What is root mean squared?
I and V are constantly changing, so cannot be assigned a fixed value over a period of time - the average would be 0.
The rms current or voltage produces the same heating effect in a resistor as the equivalent DC.
e.g. 12V DC = 12V rms AC
I(rms) = I0/√2
V(rms) = V0/√2
138
How can the mains electricity peak and
| peak-to-peak voltage values be calculated?
The electricity supplied in homes in the UK is around 230V.
The supply is alternating, so 230V is the rms value of the voltage.
V0 = V(rms) x √2 = 330V
peak-to-peak voltage = 325 x 2 = 650V
139
What is a transformer?
A transformer changes the value of an alternating voltage.
An alternating current flows in the primary coil.
This produces a changing magnetic flux in the soft iron core.
This means the flux linkage of the secondary coil is constantly changing, and so an alternating voltage is induced across it.
140
What is a step-up transformer?
Increases the AC voltage because the secondary coil has more turns than the primary coil.
141
What is a step-down transformer?
Decreases the AC voltage because the secondary coil has fewer turns than the primary coil.
142
What is the relationship between voltage and number of turns?
The ratio of the voltage in the primary coil to the secondary coil is the same as the ratio of the number of turns on the primary coil to the secondary coil.
Vs/Vp = Ns/Np
143
What is an ideal transformer?
In an ideal transformer, no energy is lost.
power supplied to primary coil = power delivered to secondary coil
VpIp = VsIs
144
What are the causes of inefficiency in a transformer?
-Eddy Currents.
These are looping currents induced by the alternating magnetic flux in the core.
Due to Lenz's Law, they create a magnetic field that acts against the field that induced them, reducing the field's flux density.
They dissipate energy by generating heat.
The effect can be reduced by laminating the core.
The core is made using layers of iron between layers of an insulator, and because the eddy currents cannot pass through the insulator, their amplitude is reduced. Eddy currents can also be reduced by using a core made out of a high resistivity metal.
-Resistance of the copper wire in the coils causes heating, resulting in a loss of energy.
This is reduced by using thick wire, which has a low resistance.
- Energy is lost if the core is not easily magnetised.
A magnetically soft iron core is used to allow easy magnetisation and demagnetisation.
145
What is the equation for efficiency in a transformer?
Not all power is transferred, so the efficiency of a transformer is the ratio between the power output and
input into it.
efficiency = IsVs/IpVp
146
What happens in real transformers?
When transferring electrical power, the power lost due to resistance is equal to I²R, therefore it is vital to reduce the current to a minimum value to prevent unnecessary energy losses.
As power = current × voltage, a low current means a high voltage for the same amount of power transmitted.
Therefore, step-up transformers are used when transmitting electricity over long distances to step up the voltage to 400kV for transmission through the National Grid.
High voltage raises safety and insulation issues, and is stepped back down to a safer 230V before it can be used in homes. This is done in stages, with power transferred from overhead lines to underground wires.
147
How can apparatus be made more sensitive to the force?
- Replace wire with coil, so the length of the wire within the magnetic field increases.
- Use asymmetrical balance, as a longer left arm would give a larger torque for the same force.
- Use a larger current, which would generate a larger magnetic force.
148
What happens when an alternating current is passed through a wire in a magnetic field?
The wire vibrates vertically.
The wire experiences a force which is perpendicular to both the magnetic flux density and the current by Fleming's left hand rule.
As the magnitude of the current varies, from a max in one direction to a max in the opposite direction, the magnitude of the force also varies.
The force acts in the opposite direction as the current reverses.
Continual reversal of AC means the process is repeated.
