Magnetic fields Flashcards

1
Q

When using Fleming’s left hand rule for moving charged particles, what happens if the charge is negative?

A

Point your second finger in the direction opposite to its motion

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2
Q

What are the units for magnetic flux?

A

Wb

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3
Q

What is the equation for the force on a particle in circular orbit?

A

F = mv²/r

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4
Q

What is the equation for the radius of the circular path of a charged particle in a magnetic field?

A

r = mv/BQ
Where:
* r = Radius (m)
* m = Mass (kg)
* v = Velocity (m/s)
* B = Magnetic flux density (T)
* Q = Charge (C)

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5
Q

Derive the equation for the radius of the circular path of a charged particle in a magnetic field.

A

Force on a charged particle in a magnetic field:
* F = BQv
Force on a particle in circular orbit:
* F = mv²/r
Therefore:
* BQv = mv²/r
* r = mv/BQ

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6
Q

In magnetic fields, what is φ?

A

Magnetic flux

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7
Q

What is the equation for the force experienced by a charged particle in a magnetic field?

A

F = BQv

Where:
* F = Force (N)
* B = Magnetic flux density (T)
* Q = Charge on particle (C)
* v = Velocity of particle (m/s)

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8
Q

Describe the structure of a cyclotron.

A

-Two hollow semi-circular electrodes with alternating potential difference.
-Slight gap between them.
-Uniform magnetic field applied perpendicular to the plane of the electrodes.

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9
Q

Describe how a cyclotron works.

A

-Particle (charged) is fired into one of the electrodes
-The magnetic field makes it flow a semi-circular path and return to the gap between electrodes
-The potential difference between them creates an electric field that accelerates the particle across the gap
-The velocity in now higher, so the particle takes a path with a larger radius before leaving the other electrode
-As it exits, the potential difference is reversed at this point so that the electric field is reversed and therefore the particle can accelerate across the gap
-This repeats as the particle spirals outwards, increasing in speed, before exiting the cyclotron

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10
Q

If p.d wasn’t alternating what would happen to the particle in a cyclotron?

A

It would slow down after leaving the second electrode

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11
Q

What is the equation for magnetic flux?

A

φ = BA

Where:
* φ = Magnetic flux (Wb)
* B = Magnetic flux density (T)
* A = Area (m²)

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12
Q

What happens when a conductor is moved in a magnetic field?

A

If it cuts through field lines, an emf is induced in the conductor:

The electrons in the rod will experience a force, which causes them to accumulate at one end of the rod - this induces an emf across the ends of the rod = electromagnetic induction.

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13
Q

Why is an emf induced in conductor when it cuts through magnetic field lines?

A

The electrons experience a force, so they accumulate at one end of the rod
This induces an emf between the positive and negative ends of the rod

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14
Q

What is electromagnetic induction?

A

When an emf is induced in a conductor that cuts through magnetic field lines.

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15
Q

How can you induce an emf in a flat coil or solenoid?

A

-Moving the coil towards it away from the poles of the magnet
-Moving a magnet towards or away from the coil

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16
Q

An emf is induced in a conductor when what is changing?

A

The magnetic field

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17
Q

What is magnetic flux linkage?

A

The product of the magnetic flux passing through the coil and the number of turn in the coil they cut the flux.

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18
Q

What are the units for magnetic flux linkage?

A

Wb turns

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19
Q

What is the equation for magnetic flux linkage when the coil is perpendicular to the field?

A

Nφ = BAN

Where:
* Nφ = Magnetic flux linkage (Wb turns)
* B = Magnetic flux density (T)
* A = Area of coil (m²)
* N = Number of turns

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20
Q

What is the equation for magnetic flux when the coil is not perpendicular to the field?

A

φ = BAcosθ

Where:
* φ = Magnetic flux (Wb)
* B = Magnetic flux density (T)
* A = Area of coil (m²)
* θ = Angle between the field and the normal of the plane of the loop
(NOTE: Not given in exam!)

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21
Q

What is the equation for magnetic flux linkage when the coil is not perpendicular to the field?

A

Nφ = BANcosθ

Where:
* Nφ = Magnetic flux linkage (Wb turns)
* B = Magnetic flux density (T)
* A = Area of coil (m²)
* θ = Angle between the field and the normal of the plane of the loop

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22
Q

Why is BANcos used instead of BAN?

What rule do we have to take into account?

A

When flux linkage isn’t perpendicular to coil of wire, we need to resolve for horizontal component because that is where you get to max force (perpendicular):

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23
Q

What does the rate of change of flux tell you?

A

How strong the emf will be in volts:

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24
Q

What can’t you do with Nφ = BAN

A
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25
Q

Describe what the difference is between:
* Magnetic flux density
* Magnetic flux
* Magnetic flux linkage

A

Magnetic flux density - The number of magnetic field lines per unit area in a magnetic field
Magnetic flux - The total number of field lines passing through a given area.
Magnetic flux linkage - The magnetic flux multiplied by the number of coils.

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26
Q

What is the symbol for magnetic flux linkage?

A

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27
Q

State Faraday’s law.

A

The magnitude of the emf induced in a conductor is directly proportional to the rate of change of flux linkage.

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28
Q

Give the equation for Faraday’s Law.

A

ε = NΔφ/Δt

Where:
* ε = Magnitude of induced emf (V)
* Nφ = Magnetic flux linkage (Wb turns)
* t = Time (s)

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29
Q

When does Faraday’s law apply?

A

Only for an object that has a changing flux - 1 flux linkage to another.

30
Q

On a graph of flux linkage against time, what does the gradient give?

A

The induced emf.

31
Q

On a graph of emf against time, what does the area under the line give?

A

Flux linkage change

32
Q

What is the equation for the emf induced in a rod passing through a magnetic field?

A

ε = Blv

Where:
* ε = Induced emf (V)
* B = Magnetic flux density (T)
* l = Length of rod (m)
* v = Velocity (m/s)
(NOTE: Not given in exam, but can be derived)

33
Q

Derive the equation for the emf induced in a rod moving at constant speed through a magnetic field.

A

When v is the velocity, A is the area covered by the loop, l is the length of the rod and d is the distance travelled by the rod:
* ε = NΔφ / Δt = ΔBAN / t
* ε = B x ΔA / t
* ε = B x l x (Δd / t)
* ε = B x l x v = Blv

34
Q

What can you think of magnetic flux as being equal to?

A

The flux cut per second.

35
Q

State Lenz’s law.

A

An induced emf is always in such a direction as to oppose the change that caused it.

36
Q

What equation do Lenz’s law and Faraday’s Law combine to give?

A

ε = -NΔφ/Δt

Where:
* ε = Magnitude of induced emf (V)
* Nφ = Magnetic flux linkage (Wb turns)
* t = Time (s)

(NOTE: Not given in exam. The equation for the magnitude of ε is given, but there is no minus sign.)

37
Q

What happens when a coil rotates in a magnetic field?

A

The coil cuts the flux and an alternating emf is induced?

38
Q

What is the amount of flux cut by the coil know as?

What is it’s equation?

A

Flux linkage:

Nφ = BANcosθ

39
Q

As the coil rotates through a magnetic field, θ changes.

As a result, what varies?

A

Flux Linkage:

Nφ = BANcosθ

40
Q

What does flux linkage vary between?

A

As changes, flux linkage varies sinusoidally (follows same pattern as sin (or cos) curve) between +BAN and -BAN.

41
Q

What is a generator?

A

A machine that uses a rotating coil in a magnetic field to convert kinetic energy into electrical energy.
They induce an electric current by rotating a coil in a magnet.

42
Q

What is another name for a generator?

A

Dynamo

43
Q

What is an alternator?

A

A generator that generates alternating current (a.c.)

44
Q

How does an a.c. generator work?

A
  • A spinning rectangular coil is placed in a magnetic field
  • Slip rings and brushes (connected to an external circuit) are connected to the coil
  • This means the direction of the induced current is
    reversed every half turn = produces an alternating current.
    The output voltage also changes with every half rotation
45
Q

As a coil in a generator rotates, what does the flux linkage vary between?

A

+BAN and -BAN

46
Q

What does the speed at which θ changes depend on?

A

Angular speed, ω

We use this in the flux linkage equation instead of θ (since θ = ωt)

47
Q

What is the equation for the the flux linkage of a coil in a generator?

A

Nφ = BANcos(ωt)

Where:
* Nφ = Magnetic flux linkage (Wb turns)
* B = Magnetic flux density (T)
* A = Area of coil (m²)
* ω = Angular velocity (rad/s)
* t = Time from coil being perpendicular to magnetic field (s)
(NOTE: Not given in exam, but Nφ = BANcosθ is given and ωt = θ)

48
Q

What does induced emf depend on?

A

The rate of change of flux linkage (Faraday’s).

Therefore it is also sinusoidal.

49
Q

What is the equation for the induced emf on a coil in a generator?

A

ε = BANωsin(ωt)

Where:
* ε = Induced emf (V)
* B = Magnetic flux density (T)
* A = Area of coil (m²)
* ω = Angular velocity (rad/s)
* t = Time from coil being perpendicular to magnetic field (s).
(observation = calculus is probably used to form this equation as seen on the graphs of emf and flux linkage)

50
Q

What is an alternating current?

A

One that is constantly changing direction with time.

51
Q

How do you compare ac and dc power output?

What can’t you do?

A

Find the average.

Normal average doesn’t work because the positive and negative bits cancel out.

Instead use root mean square voltage.

52
Q

What device can be used to show how voltage changes over time?

A

Oscilloscope

53
Q

What is the symbol for the rms voltage?

A

V(rms)

54
Q

What is the symbol for the rms current?

A

I(rms)

55
Q

What is the equation for the rms voltage?

A

V(rms) = V₀ / √2

Where:
* V(rms) = rms voltage (V
* V₀ = Peak voltage (V)
For a sine wave)

56
Q

What is the equation for the rms current?

A

I(rms) = I₀ / √2

Where:
* I(rms) = rms current (A
* I₀ = Peak current (A)
For a sine wave)

57
Q

What are transformers?

A

Devices that make use of electromagnetic induction to change the size of the voltage for an alternating current.

58
Q

Describe how a transformer works.

A

An alternating current in the primary coil causes the core to magnetise, demagnetise and remagnetise continuously in opposite directions.

This produces a rapidly changing magnetic flux.

The changing magnetic flux is passed through the iron core to the secondary coil.

This induces an alternating voltage of the same frequency as the input voltage, but different voltage (assuming the number of turns is different).

59
Q

What is the transformer equation relating the number of turns on each coil and the voltage?

A

Ns / Np = Vs / Vp

Where:
* Ns = No. of turns on secondary coil
* Np = No. of turns on primary coil
* Vs = Voltage across secondary coil
* Vp = Voltage across primary coil

60
Q

What are most power losses in a transformer due to? How does this work?

A

-Eddy currents in the transformer’s iron core are looping currents induced by the changing magnetic flux i the core.
-These create a magnetic field that acts against the field that produced them, reducing the field strength
-They also generate heat

61
Q

How can the effects of eddy currents in a transformer be reduced?

A

Laminating the core with layers of insulation so current can’t flow.

62
Q

How can heat losses due to resistance in the wires in a transformer be reduced?

A

Using thick copper wire (which has low resistance = less heat).

Copper has low resistivity and larger diameter = smaller resistance.

63
Q

Energy is wasted as it heats the core when it magnetises and demagnetises. How can this be reduced?

A

Use magnetically soft material = magnetism disappears after current is removed.

One that magnetises and demagnetises easily.

64
Q

What is the equation for an ideal transformer?

A

Power in = Power out:

65
Q

Give the equation for the efficiency of a transformer.

A

Efficiency = IsVs / IpVp

Where:
* Is = Current in the secondary coil (A)
* Vs = Potential difference across secondary coil (V)
* Ip = Current in primary coil (A)
* Vp = Potential difference across primary coil (V)

66
Q

What is the root mean squared?

A

A value of current that produces the same heating effect in a resistor as the equivalent dc

67
Q

What is an oscilloscope used for?

A

To show the sizes of voltages and currents in both dc and ac circuits

68
Q

What are eddy currents?

A

Looping currents induced by the changing magnetic flux in the core

69
Q

What do eddy currents do?

A

Create a magnetic field that acts against the field that induced them

70
Q

How do eddy currents dissipate energy?

A

By generating heat

71
Q

How can the energy loss from eddy currents be reduced?

A

By laminating the core