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Physics A Level CIE > Chapter 9 Magnetic Fields > Flashcards

Chapter 9 Magnetic Fields Flashcards

1
Q

A magnetic field is a field of force that is created either by

A
  • Moving electric charge
  • Permanent magnets
  • Permanent magnets are materials that produce a magnetic field
  • A stationary charge will not produce a magnetic field
  • A magnetic field is sometimes referred to as a B–field
  • A magnetic field is created around a current carrying wire due to the movement of electrons
  • Although magnetic fields are invisible, they can be observed by the force that pulls on magnetic materials, such as iron or the movement of a needle in a plotting compass
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2
Q

Magnetic fields are represented by

A
  • magnetic field lines
    • These can be shown using iron filings or plotting compasses
  • Field lines are best represented on bar magnets, which consist of a north pole on one end and south pole on the other
  • The magnetic field is produced on a bar magnet by the movement of electrons within the atoms of the magnet
  • This is a result of the electrons circulating around the atoms, representing a tiny current and hence setting up a magnetic field
  • The direction of a magnetic field on a bar magnet is always from north to south
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3
Q

Magnetic field lines are directed from the north pole to the south pole

A
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4
Q

When two bar magnets are pushed together, they either attract or repel each other:

A
  • Two like poles (north and north or south and south) repel each other
  • Two opposite poles (north and south) attract each other
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5
Q

The key aspects of drawing magnetic field lines:

A
  • The lines come out from the north poles and into the south poles
  • The direction of the field line shows the direction of the force that a free magnetic north pole would experience at that point
  • The field lines are stronger the closer the lines are together
  • The field lines are weaker the further apart the lines are
  • Magnetic field lines never cross since the magnetic field is unique at any point
  • Magnetic field lines are continuous
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6
Q

A uniform magnetic field is where the magnetic field strength is the

A
  • same at all points
    • This is represented by equally spaced parallel lines, just like electric fields
  • The direction of the magnetic field into or out of the page in 3D is represented by the following symbols:
    • Dots (sometimes with a circle around them) represent the magnetic field directed out of the plane of the page
    • Crosses represent the magnetic field directed into the plane of the page
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7
Q

The magnetic field into or out of the page is represented by circles with dots or crosses

A
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8
Q

A current-carrying conductor produces its own

A
  • magnetic field
    • When interacting with an external magnetic field, it will experience a force
  • A current-carrying conductor will only experience a force if the current through it is perpendicular to the direction of the magnetic field lines
  • A simple situation would be a copper rod placed within a uniform magnetic field
  • When current is passed through the copper rod, it experiences a force which makes it move
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9
Q

A copper rod moves within a magnetic field when current is passed through it

A
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10
Q

The strength of a magnetic field is known as the

A
  • magnetic flux density, B
    • This is also known as the magnetic field strength
    • It is measured in units of Tesla (T)
  • The force F on a conductor carrying current I at right angles to a magnetic field with flux density B is defined by the equation

F = BIL sinθ

  • Where:
    • F = force on a current carrying conductor in a B field (N)
    • B = magnetic flux density of external B field (T)
    • I = current in the conductor (A)
    • L = length of the conductor (m)
    • θ = angle between the conductor and external B field (degrees)
  • This equation shows that the greater the current or the magnetic field strength, the greater the force on the conductor
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11
Q

Magnitude of the force on a current carrying conductor depends on the angle of the conductor to the external B field

A
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12
Q

The maximum force occurs when

A
  • sin θ = 1
    • This means θ = 90o and the conductor is perpendicular to the B field
    • This equation for the magnetic force now becomes:

F = BIL

  • The minimum force (0) is when sin θ = 0
    • This means θ = 0o and the conductor is parallel to the B field
  • It is important to note that a current-carrying conductor will experience no force if the current in the conductor is parallel to the field
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13
Q

The direction of the force on a charge moving in a magnetic field is determined by the

A
  • direction of the magnetic field and the current
  • Recall that the direction of the current is the direction of conventional current flow (positive to negative)
  • When the force, magnetic field and current are all mutually perpendicular to each other, the directions of each can be interpreted by Fleming’s left-hand rule:
    • On the left hand, with the thumb pointed upwards, first finger forwards and second finger to the right ie. all three are perpendicular to each other
    • The thumb points in the direction of motion of the rod (or the direction of the force) (F)
    • The first finger points in the direction of the external magnetic field (B)
    • The second finger points in the direction of conventional current flow (I)
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14
Q

Fleming’s left hand rule

A
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15
Q

Using Fleming’s left-hand rule: with papers

A

B = into the page

F = vertically downwards

I = from right to left

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16
Q

The magnetic flux density B is defined as

A

The force acting per unit current per unit length on a current-carrying conductor placed perpendicular to the magnetic field

  • Rearranging the equation for magnetic force on a wire, the magnetic flux density is defined by the equation:
  • Note: this equation is only relevant when the B field is perpendicular to the current
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17
Q
  • Magnetic flux density is measured in units of tesla, which is defined as:
A

A straight conductor carrying a current of 1A normal to a magnetic field of flux density of 1 T with force per unit length of the conductor of 1 N m-1

  • To put this into perspective, the Earth’s magnetic flux density is around 0.032 mT and an ordinary fridge magnet is around 5 mT
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18
Q
  • The magnetic force on an isolating moving charge, such an electron, is given by the equation:
A

F = BQv sinθ

  • Where:
    • F = force on the charge (N)
    • B = magnetic flux density (T)
    • Q = charge of the particle (C)
    • v = speed of the charge (m s-1)
    • θ = angle between charge’s velocity and magnetic field (degrees)
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19
Q

The force on an isolated moving charge is perpendicular to its motion and the magnetic field B

A
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20
Q
  • Equivalent to the force on a wire, if the magnetic field B is perpendicular to the direction of the charge’s velocity, the equation simplifies to:
A

F = BQv

  • According to Fleming’s left hand rule:
    • When an electron enters a magnetic field from the left, and if the magnetic field is directed into the page, then the force on it will be directed upwards
  • The equation shows:
    • If the direction of the electron changes, the magnitude of the force will change too
  • The force due to the magnetic field is always perpendicular to the velocity of the electron
    • Note: this is equivalent to circular motion
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21
Q

Fleming’s left-hand rule can be used again to find the direction of the

A

force, magnetic field and velocity

  • The key difference is that the second finger representing current I (direction of positive charge) is now the direction of velocity v of the positive charge
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22
Q

The Hall voltage is a product of the

A
  • Hall effect
  • Hall voltage is defined as:

The potential difference produced across an electrical conductor when an external magnetic field is applied perpendicular to the current through the conductor

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23
Q

When an external magnetic field is applied

A
  • perpendicular to the direction of current through a conductor, the electrons experience a magnetic force
  • This makes them drift to one side of the conductor, where they all gather and becomes more negatively charged
  • This leaves the opposite side deficient of electrons, or positively charged
  • There is now a potential difference across the conductor
    • This is called the Hall Voltage, VH
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24
Q

The positive and negative charges drift to opposite ends of the conductor producing a hall voltage when a magnetic field is applied

A
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25
Q
  • An equation for the Hall voltage VH is derived from
A

the electric and magnetic forces on the charges

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26
Q

The electric and magnetic forces on the electrons are equal and opposite

A
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27
Q

The voltage arises from the

A
  • electrons accumulating on one side of the conductor slice
  • As a result, an electric field is set up between the two opposite sides
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28
Q
  • The two sides can be treated like oppositely charged parallel plates, where the electric field strength E is equal to:
A
  • Where:
    • VH = Hall voltage (V)
    • d = width of the conductor slice (m)
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29
Q

A single electron has a drift velocity of v within the conductor. The magnetic field is into the plane of the page, therefore the electron has a magnetic force FB to the right:

A

FB = Bqv

  • This is equal to the electric force FE to the left:

FE = qE

qE = Bqv

  • Substituting E and cancelling the charge q

VH/d = Bv

  • Recall that current I is related to the drift velocity v by the equation:

I = nAvq

  • Where:
    • A = cross-sectional area of the conductor (m2)
    • n = number density of electrons (m-3)
  • Rearranging this for v and substituting it into the equation gives:

VH/d = B(I/nAq)

  • The cross-sectional area A of the slice is the product of the width d and thickness t:

A = dt

  • Substituting A and rearranging for the Hall voltage VH leads to the equation:

VH/d = B(I/n(dt)q)

VH/d = B(I/ntq)

  • Where:
    • B = magnetic flux density (T)
    • q = charge of the electron (C)
    • I = current (A)
    • n = number density of electrons (m-3)
    • t = thickness of the conductor (m)
  • This equation shows that the smaller the electron density n of a material, the larger the magnitude of the Hall voltage
    • This is why a semiconducting material is often used for a Hall probe
  • Note: if the electrons were placed by positive charge carriers, the negative and positive charges would still deflect in opposite directions
    • This means there would be no change in the polarity (direction) of the Hall voltage
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30
Q

A Hall probe can be used to measure the

A
  • magnetic flux density between two magnets based on the Hall effect
  • It consists of a cylinder with a flat surface at the end
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31
Q

A Hall probe consists of a flat surface and is held so the magnetic field lines are perpendicular to it

A
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32
Q

A Hall probe consists of a flat surface and is held so the magnetic field lines are perpendicular to it

A
  • the flat surface of the probe must be directed between the magnets so the magnetic field lines pass completely perpendicular to this surface
  • The probe is connected to a voltmeter to measure the Hall voltage
  • If the probe is not held in the correct orientation (perpendicular to the field lines), the voltmeter reading will be reduced
  • Since the Hall voltage is directly proportional to the magnetic flux density, the flux density of the magnets can be obtained
  • A Hall probe is sensitive enough to measure even the Earth’s magnetic flux density
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33
Q

The Hall voltage depends on

A

angle between the magnetic field and the plane of the probe

34
Q

The Hall voltage reaches a maximum when the

A

field is perpendicular to the probe

35
Q

The Hall voltage is zero when the field is

A
  • parallel to the probe
36
Q

A charged particle in uniform magnetic field which is perpendicular to its direction of motion travels in a

A
  • circular path
  • This is because the magnetic force FB will always be perpendicular to its velocity v
    • FB will always be directed towards the centre of the path
37
Q
  • The magnetic force FB provides the centripetal force on the particle
A
  • Recall the equation for centripetal force:

F= Mv2/r

  • Where:
    • m = mass of the particle (kg)
    • v = linear velocity of the particle (m s-1)
    • r = radius of the orbit (m)
  • Equating this to the force on a moving charged particle gives the equation:

Mv2/r = Bqv

  • Rearranging for the radius r obtains the equation for the radius of the orbit of a charged particle in a perpendicular magnetic field:

r = mv/Bq

  • This equation shows that:
    • Faster moving particles with speed v move in larger circles (larger r): r ∝ v
    • Particles with greater mass m move in larger circles: r ∝ m
    • Particles with greater charge q move in smaller circles: r ∝ 1 / q
    • Particles moving in a strong magnetic field B move in smaller circles: r ∝ 1 / B
38
Q
  • A velocity selector is:
A

A device consisting of perpendicular electric and magnetic fields where charged particles with a specific velocity can be filtered

39
Q

Velocity selectors are used in devices, such as

A

mass spectrometers, in order to produce a beam of charged particles all travelling at the same velocity

40
Q

The construction of a velocity selector consists of two

A

horizontal oppositely charged plates situated in a vacuum chamber

  • The plates provide a uniform electric field with strength E between them
41
Q

There is also a uniform magnetic field with flux density B applied perpendicular to the electric field

A
    • If a beam of charged particles enter between the plates, they may all have the same charge but travel at different speeds v
  • The electric force does not depend on the velocity: FE = EQ
  • However, the magnetic force does depend on the velocity: FB = BQv
    • The magnetic force will be greater for particles which are travelling faster
  • To select particles travelling at exactly the desired the speed v, the electric and magnetic force must therefore be equal, but in opposite directions

FE = FB

42
Q

The particles travelling at the desired speed v will travel through undeflected due to the equal and opposite electric and magnetic forces on them

A
43
Q

The resultant force on the particles at speed v will be

A
  • zero, so they will remain undeflected and pass straight through between the plates
  • By equating the electric and magnetic force equations:

EQ = BQv

  • The charge Q will cancel out on both sides to give the selected velocity v equation:

V= E/B

  • Therefore, the speed v in which a particle will remain undeflected is found by the ratio of the electric and magnetic field strength
    • If a particle has a speed greater or less than v, the magnetic force will deflect it and collide with one of the charged plates
    • This would remove the particles in the beam that are not exactly at speed v
44
Q

the gravitational force on the charged particles will be negligible compared to the

A

electric and magnetic forces and therefore can be ignored in these calculations

45
Q

Magnetic field patterns are not only observed around bar magnets, magnetic fields are formed wherever current is flowing, such as in:

A
  • Long straight wires
  • Long solenoids
  • Flat circular coils
46
Q

Field Lines in a Current-Carrying Wire

A
  • Magnetic field lines in a current carrying wire are circular rings, centered on the wire
  • The field lines are strongest near the wire and become further part away from the wire
  • Reversing the current reverses the direction of the field
47
Q

The direction of the magnetic field is determined by

A

Maxwell’s right hand screw rule

  • This is determined by pointing the right-hand thumb in the direction of the current in the wire and curling the fingers onto the palm
  • The direction of the curled fingers represents the direction of the magnetic field around the wire
  • For example, if the current is travelling vertically upwards, the magnetic field lines will be directed anticlockwise, as seen from directly above the wire
  • Note: the direction of the current is taken to be the conventional current ie. from positive to negative, not the direction of electron flow
48
Q

Field Lines in a Solenoid

A
  • As seen from a current carrying wire, an electric current produces a magnetic field
  • An electromagnetic makes use of this by using a coil of wire called a solenoid which concentrates the magnetic field
  • One ends becomes a north pole and the other the south pole
49
Q

, the magnetic field lines around a solenoid are very similar to a bar magnet how?

A
    • The field lines emerge from the north pole
      • The field lines return to the south pole
  • Which is the north or south pole depends on the direction of the current
    • This is found by the right hand grip rule
  • This involves gripping the electromagnet so the fingers represent the direction of the current flow of the wire
  • The thumb points in the direction of the field lines inside the coil, or in other words, point towards the electromagnet’s north pole
50
Q

Field Lines in a Flat Circular Coil

A
  • A flat circular coil is equal to one of the coils of a solenoid
  • The field lines will emerge through one side of the circle (north pole) and leave the other (south pole)
  • As before, the direction of the north and south pole depend on the direction of the current
    • This can be determined by using the right hand thumb rule
    • It easier to find the direction of the magnetic field on the straight part of the circular coil to determine which direction the field lines are passing through
51
Q

Factors Affecting Magnetic Field Strength

A
  • The strength of the magnetic field of a solenoid can be increased by:
    • Adding a core made from a ferrous (iron-rich) material eg. an iron rod
    • Adding more turns in the coil
  • When current flows through the solenoid with an iron core, it becomes magnetised, creating an even stronger field
    • The addition of an iron core can strengthen the magnetic field up to a several hundred times more
  • When more turns are added in the coil, this concentrates the magnetic field lines, causing the magnetic field strength to increase
52
Q

Newton’s Third Law states

A
  • When two bodies interact, the force on one body is equal but opposite in direction to the force on the other body
  • Therefore, the forces on the wires act in equal but opposite directions
53
Q

A current carrying conductor, such as a wire, produces a

A
  • magnetic field around it
  • The direction of the field depends on the direction of the current through the wire
    • This is determined by the right hand thumb rule
54
Q

Parallel current-carrying conductors will therefore either

A

attract or repel each other

  • If the currents are in the same direction in both conductors, the magnetic field lines between the conductors cancel out – the conductors will attract each other
  • If the currents are in the opposite direction in both conductors, the magnetic field lines between the conductors push each other apart – the conductors will repel each othe
55
Q

Both wires will attract if their currents are in the same direction and repel if in opposite directions

A
  • When the conductors attract, the direction of the magnetic forces will be towards each other
  • When the conductors repel, the direction of the magnetic forces will be away from each other
  • The magnitude of each force depend on the amount of current and length of the wire
56
Q

Electromagnetic induction is when an

A
  • e.m.f is induced in a closed circuit conductor due to it moving through a magnetic field
  • This happens when a conductor cuts through magnetic field lines
  • The amount of e.m.f induced is determined by the magnetic flux
57
Q

The amount of magnetic flux varies as the coil rotates within the field

A
  • The flux is the total magnetic field that passes through a given area
  • It is a maximum when the magnetic field lines are perpendicular to the area
  • It is at a minimum when the magnetic field lines are parallel to the area
58
Q
  • The magnetic flux is defined as:
A

The product of the magnetic flux density and the cross-sectional area perpendicular to the direction of the magnetic flux density

  • In other words, magnetic flux is the number of magnetic field lines through a given area
59
Q

Magnetic flux is defined by the symbol

A
  • Φ (greek letter ‘phi’)
  • It is measured in units of Webers (Wb)
  • Magnetic flux can be calculated using the equation:

Φ = BA

  • Where:
    • Φ = magnetic flux (Wb)
    • B = magnetic flux density (T)
    • A = cross-sectional area (m2)
60
Q
  • When the magnet field lines are not completely perpendicular to the area A, then the component of magnetic flux density B perpendicular to the area is taken
  • The equation then becomes:
A

Φ = BA cos(θ)

  • Where:
    • θ = angle between magnetic field lines and the line perpendicular to the plane of the area (often called the normal line) (degrees)
61
Q
  • This means the magnetic flux is:
    • Maximum and Minimum at?
A
  • Maximum = BA when cos(θ) =1 therefore θ = 0o. The magnetic field lines are perpendicular to the plane of the area
  • Minimum = 0 when cos(θ) = 0 therefore θ = 90o. The magnetic fields lines are parallel to the plane of the area
62
Q

An e.m.f is induced in a circuit when the

A

magnetic flux linkage changes with respect to time

  • This means an e.m.f is induced when there is:
    • A changing magnetic flux density B
    • A changing cross-sectional area A
    • A change in angle θ
63
Q

The magnetic flux linkage is a quantity commonly used for

A
64
Q

Magnetic flux linkage is defined as: and is calculated using the equation:

A

The product of the magnetic flux and the number of turns

  • It is calculated using the equation:

ΦN = BAN

  • Where:
    • Φ = magnetic flux (Wb)
    • N = number of turns of the coil
    • B = magnetic flux density (T)
    • A = cross-sectional area (m2)
  • The flux linkage ΦN has the units of Weber turns (Wb turns)
  • As with magnetic flux, if the field lines are not completely perpendicular to the plane of the area they are passing through
  • Therefore, the component of the flux density which is perpendicular is equal to:

ΦN = BAN cos(θ)

65
Q

Magnetic flux linkage is defined as: and is calculated using the equation:

A

The product of the magnetic flux and the number of turns

  • It is calculated using the equation:

ΦN = BAN

  • Where:
    • Φ = magnetic flux (Wb)
    • N = number of turns of the coil
    • B = magnetic flux density (T)
    • A = cross-sectional area (m2)
  • The flux linkage ΦN has the units of Weber turns (Wb turns)
  • As with magnetic flux, if the field lines are not completely perpendicular to the plane of the area they are passing through
  • Therefore, the component of the flux density which is perpendicular is equal to:

ΦN = BAN cos(θ)

66
Q

Electromagnetic induction is a

A
  • phenomenon which occurs when an e.m.f is induced when a conductor moves through a magnetic field
  • When the conductor cuts through the magnetic field lines:
    • This causes a change in magnetic flux
    • Which causes work to be done
    • This work is then transformed into electrical energy
  • Therefore, if attached to a complete circuit, a current will be induced
67
Q

electromagnetic induction and is defined as:

A

The process in which an e.m.f is induced in a closed circuit due to changes in magnetic flux

  • This can occur either when:
    • A conductor cuts through a magnetic field
    • The direction of a magnetic field through a coil changes
68
Q

Electromagnetic induction is used in:

A
    • Electrical generators which convert mechanical energy to electrical energy
      • Transformers which are used in electrical power transmission
  • This phenomenon can easily be demonstrated with a magnet and a coil, or a wire and two magnets
69
Q

Moving a magnet through a coil

Factors that will increase the induced e.m.f are:

A
  • Moving the magnet faster through the coil
  • Adding more turns to the coil
  • Increasing the strength of the bar magnet
70
Q

An e.m.f is induced only when the bar magnet is moving through the coil

A
71
Q

A wire is moved between two magnets connected to a voltmeter to induce an e.m.f

A
72
Q

Experiment 1: Moving a magnet through a coil expected results

A
  • When the bar magnet is not moving, the voltmeter shows a zero reading
    • When the bar magnet is held still inside, or outside, the coil, the rate of change of flux is zero, so, there is no e.m.f induced
  • When the bar magnet begins to move inside the coil, there is a reading on the voltmeter
    • As the bar magnet moves, its magnetic field lines ‘cut through’ the coil, generating a change in magnetic flux
    • This induces an e.m.f within the coil, shown momentarily by the reading on the voltmeter
  • When the bar magnet is taken back out of the coil, an e.m.f is induced in the opposite direction
    • As the magnet changes direction, the direction of the current changes
    • The voltmeter will momentarily show a reading with the opposite sign
  • Increasing the speed of the magnet induces an e.m.f with a higher magnitude
    • As the speed of the magnet increases, the rate of change of flux increases
  • The direction of the electric current, and e.m.f, induced in the conductor is such that it opposes the change that produces it
73
Q

Experiment 2: Moving a wire through a magnetic field expected results

A
  • When the wire is not moving, the voltmeter shows a zero reading
    • When the wire is held still inside, or outside, the magnets, the rate of change of flux is zero, so, there is no e.m.f induced
  • As the wire is moved through between the magnets, an e.m.f is induced within the wire, shown momentarily by the reading on the voltmeter
    • As the wire moves, it ‘cuts through’ the magnetic field lines of the magnet, generating a change in magnetic flux
  • When the wire is taken back out of the magnet, an e.m.f is induced in the opposite direction
    • As the wire changes direction, the direction of the current changes
    • The voltmeter will momentarily show a reading with the opposite sign
  • As before, the direction of the electric current, and e.m.f, induced in the conductor is such that it opposes the change that produces it
74
Q

When Moving a wire through a magnetic field Factors that will increase the induced e.m.f are:

A
  • Increasing the length of the wire
  • Moving the wire between the magnets faster
  • Increasing the strength of the magnets
75
Q

Faraday’s law tells us the

A
  • magnitude of the induced e.m.f in electromagnetic induction and is defined as:

The magnitude of the induced e.m.f is directly proportional to the rate of change in magnetic flux linkage

76
Q

Faraday’s law equation

A
  • Where:
    • ε = induced e.m.f (V)
    • N = number of turns of coil
    • Δɸ = change in magnetic flux (Wb)
    • Δt = time interval (s)
77
Q

Lenz’s Law gives the

A
  • direction of the induced e.m.f as defined by Faraday’s law:

The induced e.m.f acts in such a direction to produce effects which oppose the change causing it

  • Lenz’s law combined with Faraday’s law is:
  • This equation shows:
    • When a bar magnet goes through a coil, an e.m.f is induced within the coil due to a change in magnetic flux
    • A current is also induced which means the coil now has its own magnetic field
    • The coil’s magnetic field acts in the opposite direction to the magnetic field of the bar magnet
78
Q

If a direct current (d.c) power supply is replaced with an alternating current (a.c) supply, the e.m.f induced will also be

A

alternating with the same frequency as the supply

79
Q

Showing that F= BIL and F = BQV are consistent with one another

A

-We know that I = Q/T -Sub for I in F = BIL - F= BQL/T -but L/t = velocity -F= BQV AND F= BEW FOR AN ELECTRON

80
Q

The equation F= BEV on a charged particle

A

Tells us perspective on all the electrons within a conductor ( wire )

81
Q

The charge to mass ratio of an electron

A

r= m(electron)v/Be = e/m(electron) = V/B

82
Q

Speed of electrons

A

We use the cathode voltage to measure b and r The cathode and anode voltage is the Vca is the pd between them which cause each electron to accelerate as it moves from the cathode to the anode W= eVca W= 1/2Mev^2 r= MeV/ Be (1) 1/2mev^2 = eVca (2) Vca = 1/2B^2R^2/Me (3) Vca= 1/2 x B^2er^2/Me

Physics A Level CIE (14 decks)

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