Fields Flashcards
1
Q
Similarities and Differences between Gravitational Fields and Electric Fields
A
Similarities:
- both have inverse-square laws
-
Differences:
- masses always attract, charges can both attract and repel
2
Q
What is a Force Field?
A
A region in which a body experiences a non-contact force
e.g the gravitational field
3
Q
Field Lines
A
- field lines are lines of force
- ## field line directions are presented based on the positive charge, meaning they emanate out of positive charges and inwards for negative charges
4
Q
State Newton’s Law of Gravitation
A
- The force of attraction between two point masses
- is proportional to the product of the two masses
- and inversely proportional to the square of the distances between them
F = GMm/r^2
5
Q
What is g?
A
The strength of a gravitational field, g, is the force per unit mass in a small test mass placed in the field
and also the acceleration of a falling object when under freefall
6
Q
A
7
Q
What is Gravitational Potential Energy?
A
- the energy of an object due to its position in a gravitation field
8
Q
What is the Gravitational Potentialv
A
The work done per unit mass to move a small object from infinity to that point
9
Q
What is a Potential Gradient?
A
- the potential gradient at a point in a gravitational field is the change of potential per metre at that point
- potential gradient = V/r (for small distances of r)
- gravitational field strength is the negative of the potential gradient
10
Q
Hall Probes
A
- hall probes are used to measure magnetic flux density
- they contain a slice of semiconducting material
how it works:
- a constant current passes through
- the charge carriers are deflected by the magnetic field
- a potential difference (hall voltage) is created between the top and bottom edges of the slice ( this is the hall effect )
- once the hall effect occurs charge carriers passing through the probe no longer are deflected because the forced caused by the magnetic field is opposed by the force of the electric field.
- the voltage produced is proportional to the magnetic flux density (provided a constant current)
11
Q
Escape Velocity (from a planet)
A
- the escape velocity from a planet is the minimum velocity an object must be given to escape from the planet when projected vertically from the surface
- if an object is projected at speed v
1/2mv^2 > ΔW
1/2mv^2 > GMm/R
so v^2 > 2GM/R
so escape v = (2GM/R)^1/2
g = GM/(R^2)
∴ Vesc = (2gR)^1/2
12
Q
Why is the gravitational field strength linear from 0-R of the earths radius?
A
At the Earth’s center, g is zero. As the point goes away from the centre, the gravitational field strength increases in proportion to the distance.
where mass = density x volume
so enclosed mass = (4 /3)pir^3
13
Q
Satellites
A
- Any large mass that orbits a larger mass is a satellite e.g the moon is a natural satellite of the earth
- Geostationary/Geosynchronous satellites orbit the earth directly above the equator
- this is because it has a time period of exactly 24HRS so if it had the same time period as the earth’s rotation
radius of orbit can be found r^3/T^2=GM/4π^2
- this is because it has a time period of exactly 24HRS so if it had the same time period as the earth’s rotation
- Polar Orbits
- low orbit
14
Q
A
- the force of gravitational attraction between each planet and the sun is the centripetal force that keeps the planet on its orbit
- GM/r^2 = v^2/r where M is the mass of the sun
- v^2 = GM/r
- v = 2πr/T
- (2πr)^2/T^2 = GM/r
therefore
r^3/T^2 = GM/4π^2
and because GM/4π^2 is the same for all planets then r^3/T^2 is the same for all of the planets
15
Q
A
KE = 1/2 mv^2 = 1/2mx GM/r = GMm/2r
V = -GM/r
Ep = mV = - GMm/r
= -GMm/r + GMm/2r = -GMm/2r
E = -GMm/2r
16
Q
What is the Electric Field Strength?
A
- The force per unit charge on a positive test charge placed at that point
- units NC^1
- F= EQ
where E is field strength, F is force and Q is charge - the electric field strength is a before in the same direction as the force on a positive test charge
17
Q
A
- uniform
- parallel to each other
- at right angles to the plates
- from the positive plate to the negative plate
18
Q
The force in a small test charge in an electric field is…
A
- In the same direction as the electric field if the charge is positive
- In the opposite direction to the electric field if the charge is negative
19
Q
Why must a test charge need to very much less than 1 Coulomb?
A
- this amount if charge would affect the charges that cause the field, and so it would alter the electric field and its field strength
20
Q
A
- For a charged metal conductor, the charge on it is spread across its surface
- the more concentrated the charge is on the surface, the greater the strength of the electric field above the surface
21
Q
Electric potential
A
- The work done per unit positive charge on a positive test charge when it is moved from infinity to that position in the field
where V = EPE/Q
22
Q
A
- Equipotentials are surfaces of constant potential
- a test charge moving along an equipotential has constant potential energy
- no work is done by the electric field on the test charge because the force due to the field is at right angles to the equipotentials
23
Q
Potential Gradients
A
- the potential gradient at any position in an electric field is the change in potential per unit charge of distance in a given direction
- the closer the equipotentials are the greater the potential gradient is (at right angles to the equipotentials)
- the electric field strength is equal to the negative of the potential gradient
24
Q
A
- The gravitational potential in a gravitational field is always negative because it’s attractive
- the electric potential in the electric field near a point charge Q can be both positive or negative according to whether Q is a positive or negative charge
25
What is the Motor Effect?
- A current-carrying wire placed at a non-zero angle to the lines of force of an external magnetic field experiences a force due to the field
- The force is perpendicular to the wire and to the lines of force
26
- the magnitude of the force depends on:
- the current
- strength of the magnetic field
- the length of wire
- the force is:
- greatest when the wire is at right angles to the magnetic field
- zero when the wire is parallel to the magnetic field
27
Couple in a coil in a magnetic field
- each wire experiences BIl where l is the length of each long side
- each long side experience a horizontal force F = (BIl)n in the opposite directions at right angles to the field lines
- the pair of forces acting on the long sides form a couple as they are not directed along the same line
- the torque of the couple = Fd
28
- the beam follows a circular path because the direction of the force on each electron is perpendicular to the direction of motion of the electron (and field direction)
29
- The electrons moving along the current-carrying wire are pushed to one side by the force of the field
- the electrons being confined to a wire cause the whole wire to move downwards
30
- the force of the magnetic field on a moving charged particle is at right angles to the direction of motion of the particle
- No work is done by the magnetic field on the particle as the force always acts perpendicular to the velocity of the particle
- the kinetic energy of a particle is unchanged by the magnetic field
- the force causes a centripetal acceleration
-m
31
How can radius of curvature for a particle under a magnetic field be used to determine the particle
r = mv/BQ
- the larger the radius the greater the mass of the particle
- the smaller the charge the smaller the radius
32
How can you increase the induced EMF of a wire?
- move the wire faster
- use a stronger magnet
- make a wire into a coil
- pushing the magnet in or out of the coil
33
How to increase Efficiency of a transformer
- thick copper wire to reduce resistance due to wire
- EMF may be induced in the iron causing eddy currents which will resist the flow of charge and emit heat, laminate the layers to prevent it
-
34
35
Len’s Law states
- the direction of the induced current is always such as to oppose the change that causes the current
36
Faraday again lawl
- law of electromagnetic induction states that the induced emf in a circuit is equal to the rate of change of flux linkage through the circuit
37
Loaded and Unloaded Motors
- An unloaded motor will spin with a high speed
- the rate of change of flux linkage is high so the induced **back** EMF will be high.
- there is small potential difference between the **back** EMF and EMF causing the motor to spin
- thus the resulting current is low
- The speed is limited by resistive forces (bearing friction and air resistance)
- little power used
38
Loaded Motors
- A loaded motor will spin with a low speed
- the rate of change of flux linkage is low
- induced back EMF will be low
- there is a large potential between the back EMF and the EMF
- causing the motor to spin and the resulting current is high
- Power is transferred from the voltage source to mechanical power in the load and wasted heat due to resistance
39
Len’s Law
- The induced/Back EMF will always oppose or tend to oppose the flux change produced
40
- When a magnet i pushed in to a coil the induced EMF opposes the motion by producing a field which repels the magnet
- when you remove the magnet from the coil the induced emf opposes this motion by producing a field that attracts the magnet
- in both case work must be done to move the magnet
- this work is what transfers energy to a component
41
Coil Attached to Oscilloscope (update)
- A magnet is dropped through a coil that is connected to an oscilloscope
-
in the case below:
the emf at A is smaller than the emf at C because the magnet will be moving faster ( because the magnet is being accelerated due to gravity), so more flux linkage cut
42
Faraday’s Law
- EMF is proportional to the rate of change of flux linkage
43
44
What causes the magnetic field of the Earth?
- The Earth’s magnetic field is produced by the movement of the ferrous compounds in the mantle core
- this causes the magnetic field of the earth to be at angle and constantly moving
45
Define Magnetic Flux Density
- Fore per unit current per unit length that acts on a current-carrying conductor to the magnetic field
46
Define a Tesla and it’s SI base units
B = F/IL -> 1N/1A 1m
kgsA^-1^-2
47
When can you not use the F=BQv equation?
- When the velocity is NOT perpendicular to the field
- to find the velocity perpendicular to the field -> F = BQvsinθ
48
Explain why charged particles in a magnetic field follow a circular path
- The Force is perpendicular to the velocity
- So a charged particle in motion will experience a constant perpendicular force to a centre, that acts as a centripetal force on the particle
- this causes the particle to follow a circular path
49
Why do electrons follow a circular path opposite
- Fleming’s Left hand Rule uses conventional current
- the current thus for electrons in motion is in the opposite direction and thus experiences a perpendicular force in the opposite direction
- this constant perpendicular force caused by the magnetic field acts as centripetal force causing circular motion
50
Derive the equation to find the radius of curvature for a charged particle in motion
- F = mv^2/r
- F = BQv
- BQv = mv^2/r
- r = mv/BQ
51
- The force due to the uniform magnetic field is perpendicular the direction of travel
- This will be the net centripetal force and the particle will experience circular motion
52
What is the path of a charged particle moving in a uniform electric field?
A parabola
53
Define Magnetic Flux
magnetic flux is the product of the magnetic flux density perpendicular to an area and the area itself
φ = B A cos θ
B, magnetic flux density perpendicular to area
θ, angle between normal and resultant B
(if ever given angle between B and horizontal, use sinθ OR cos(90-θ)
A, the area
54
Define Magnetic Flux Linkage
N φ = NBAcos θ
units -> Wb, Wb Turns
55
When is Magnetic Flux at a maximum?
- B is parallel to the normal/perpendicualr to the area
- φ = BA cos (0) -> φ = BA
56
When is magnetic flux at a minimum?
- B (magnetic flux density) is perpendicular to the normal/ parallel to the area
- φ = BA cos(90) = 0
57
What direction does a magnetic field go from
- North to South
58
State Faraday’s Law
- The **induced** EMF is directly proportional to the **rate of change** of magnetic flux linkage
59
State Lenz’s Law
- The direction of the induced emf is such that to oppose the change that is producing it
60
Why are current carrying wires able to interact with a magnetic field?
- Each current-carrying wire produces its own magnetic field
61
Why is induced emf always in the opposite direction to the direction of the magnetic flux linkage
- Lenz’s Law
62
State and Explain what occurs to the poles of a current-carrying wire when the north pole of a magnet is sent towards it
- Lenz’s Law - The direction of the induced EMF is such that to oppose the change that is producing it
- therefore a Northpole will be produced at the end of the wire
63
State and Explain what occurs to the poles of a current-carrying wire when the north pole of a magnet is sent away from it
- Lenz’s Law: The direction of the induced EMF is such that to oppose the change that is producing it
- therefore a Southpole will be produced at the end of the wire to attract it back
64
State and Explain what occurs to the poles of current-carrying wire when the north pole of a magnet is stationary in front of it
- Nothing
- There is no EMF induced to oppose a change caused by the magnet because the magnet is not in motion
- there is no change in flux linkage so no induced EMF
65
Why are planes/aircrafts able to induce an EMF between their wing tips
- The earth has its own magnetic field (due to the molten material in the earth’s core)
- Planes/Aircrafts fly perpendicular to the field and thus the area of their wings is perpendicular to the field
- φ = BANcos θ
where B is the perpendicular magnetic flux density to the area
- there is thus flux linkage
- as the plane is in motion there is a rate of change of flux linkage between the wing tips **due to a change in area per second**
- according to Len’s Law an EMF is induced in a direction such that to oppose a change to the magnetic flux linkage
- ε = ΔBA/Δt = Bl • X/Δt , X/Δt = v
- (where x is the distance travelled in 1s)
- ε = Blv
- so an EMF is induced across the wing tips
66
EMF induced in a coil rotating uniformly in a magnetic field
- N φ = BANcos θ
(where B is perpendicular to the area)
- There is a constant change in angular displacement, where θ is the angle between B and the normal to the area
- rate of change of θ = ω
- therefore, N φ = BANcos ωt
- ( or **BANωsin ωt**)
67
What is an alternating current?
- An electric current that **reverses** its direction many times a second at regular intervals
68
Key between Difference Battery and Generator
- Battery provides direct current
- Generator provides alternating current
69
How can the rms Voltage be found from the peak voltage?
Vrms = Vo/ ( (2)^1/2)
70
What is the rms Voltage
- The most likely voltage for a application to be over time
e.g mains ≈ 230
71
How can the Average Power be calculated using peak voltage and peak current?
- Irms = Io/ ( (2)^1/2)
- Vrms = Vo/ ( (2)^1/2)
P(average) = Irms x Vrms
72
Explain the operation of a Transformer
Primary: AC current runs through the primary coil. The magnetic field and hence magnetic flux linkage around the primary coil is changing
Core: It provides a great magnetic flux linkage from the primary to the secondary coil
Secondary Coil: The changing magnetic flux passes through it, inducing an emf that is determined by the number of turns in the primary and secondary coil
73
Why is a core important to a transformer?
- The core provides a greater magnetic flux linkage from the primary to the secondary coil
- It means less of the field is wasted to its surroundings
- making the transformer more efficient
74
State the transformer equations
Ns/Np = Vs/Vp = **Ip/Is**
For an ideal transformer Pp = Ps
so VpIp = VsIs
so Vs/Vp = Ip/Is
75
Efficiency of a transformer (non-ideal)
Ps/Pp = IsVs/IpVp
76
Inefficiencies in a Transformer
- Magnetic Flux cuts through the metallic core and this can induce EMF and hence currents - eddy currents
- They dissipate heat and reduce the efficiency in a transformer
- The efficiency can be improved by **laminating** the core - layers of insulator within the core which limit the effects of eddy currents
77
What is a transformer?
- A device that changes high alternating voltage at low current to low alternating voltage at high current
78
What is an Equipotential?
- A region for which the potential of a field is a field
- and thus the work done moving along this potential is always 0
