Rate of change of the magnetic field

Definition

Induced potential difference

An induced potential difference is the potential difference produced across the ends of a conductor by a changing magnetic field.

Definition

Induced current

An induced current is the current driven by an induced potential difference when the conductor forms part of a complete circuit.

The size of the induced potential difference is set by the rate at which the magnetic field through the conductor changes, not by the size of the field itself.
A change completed in a shorter time gives a larger induced potential difference, and the same change spread over a longer time gives a smaller one.
Anything that makes the field through the coil change by a larger amount, or change in a shorter time, increases the induced potential difference.
The induced current grows in proportion to the induced potential difference for a fixed circuit resistance, so the same list of factors controls the current reading.
Each factor works by changing either how much the field through the coil changes or how quickly that change happens.

The five controlling factors

Speed of relative movement:
1. Moving the magnet or the coil faster completes the same change in the field in less time, so the rate of change is greater.
2. Doubling the speed roughly doubles the peak induced potential difference for the same magnet and coil.
Number of turns on the coil:
1. Each turn of wire has a potential difference induced across it, and the turns are joined in series, so their contributions add together.
2. A coil of $200$ turns gives about twice the induced potential difference of an otherwise identical coil of $100$ turns.
Strength of the magnetic field:
1. A stronger magnet, or two magnets used together, produces a larger change in the field for the same movement.
2. Slotting a soft iron core into the coil concentrates the field lines through the coil and increases the induced potential difference sharply.
Area of the coil:
1. A coil of larger cross-sectional area has more of the magnetic field passing through it, so the same movement changes the field through it by more.
Orientation of the movement:
1. Moving a wire at right angles to the field lines makes it cut through the greatest number of them and gives the largest induced potential difference.
2. Moving a wire along the field lines makes it cut none of them, so nothing is induced.

Factors that make no difference

The resistance of the external circuit changes the induced current but not the induced potential difference.
The material of the wire changes the resistance of the coil, so it affects the current rather than the induced potential difference.
The length of time for which the magnet is left inside the coil makes no difference once it has stopped moving, because the reading has already fallen to zero.
The absolute position of the magnet matters only through how much the field through the coil changes as it moves.

Practical

Investigating what changes the induced potential difference

Aim: to find how the peak induced potential difference depends on the speed of movement, the number of turns on the coil and the strength of the magnetic field.
Apparatus: two or three coils of known turns such as $100$ , $200$ and $400$ turns, identical bar magnets, a vertical plastic tube of about $m1\ \text{m}$ , a data logger with a voltage sensor set to record at a high sampling rate, soft iron core, retort stand and clamp, metre rule, foam landing pad and connecting leads.
Variables, speed investigation: the drop height above the coil is the independent variable, the peak induced potential difference is the dependent variable, and the same magnet, coil, number of turns and sampling rate are controlled.
Variables, turns investigation: the number of turns on the coil is the independent variable, the peak induced potential difference is the dependent variable, and the drop height, magnet and coil diameter are controlled.
Method, setting up:
- Clamp the plastic tube vertically and slide the coil onto it so that the magnet must fall straight through the middle of the coil.
- Connect the coil to the voltage sensor and set the data logger to record for a short interval at a high sampling rate so the pulse shape is captured.
- Place a foam pad at the bottom of the tube so the magnet is not damaged when it lands.
- Use the metre rule to mark release heights on the tube, measured from the top of the coil.
Method, changing the speed:
- Release the magnet from the lowest marked height without pushing it, and record the peak induced potential difference from the trace.
- Repeat the drop three times from that height and calculate a mean peak value.
- Repeat for at least five increasing release heights, which give increasing speeds at the coil.
- Calculate the speed at the coil for each height using $v=2ghv=\sqrt{2gh}$ so that speed can be plotted rather than height.
Method, changing the number of turns:
- Fix one release height and use it for every coil so the speed at the coil is the same each time.
- Swap the coil for one with a different number of turns, keeping the coil diameter and the magnet the same.
- Take three drops with each coil and record the mean peak induced potential difference.
Method, changing the field strength:
- Repeat one fixed drop with a single magnet, then with two identical magnets held with like poles together to give a stronger field.
- Repeat the fixed drop with a soft iron core inserted into the coil and compare the peak value with the empty coil.
Measurements and processing: tabulate release height, calculated speed, number of turns and the three peak readings with their mean, then plot peak induced potential difference against speed and against number of turns.
Expected pattern: both graphs are straight lines through the origin, the stronger field gives a larger peak at the same speed, and the soft iron core gives the largest increase of all.
Sources of uncertainty: the magnet may tilt or rub inside the tube, the data logger may miss the true peak if the sampling rate is too low, the coil may shift on the tube between runs, and the magnet may lose speed to air resistance.
Improvements: use light gates to measure the actual speed at the coil rather than calculating it, raise the sampling rate until the peak value stops changing, and secure the coil to the tube so it cannot move.
Safety: clamp the tube so it cannot fall, keep magnets away from cards and phones, and stand clear of the base of the tube while a magnet is falling.

Reading the graphs and traces

A straight line through the origin on a graph of peak induced potential difference against speed shows that the two quantities are directly proportional.
A straight line through the origin on a graph of peak induced potential difference against number of turns shows the same proportional relationship for the turns.
Doubling the speed makes the pulse on an oscilloscope twice as tall and half as wide, because the same overall change in the field happens in half the time.
The area under a pulse of induced potential difference against time barely changes when only the speed changes, since the total change in the field is the same.
Reading a value off a straight line through the origin is a matter of scaling, so a coil of triple the turns at double the speed gives six times the original peak.

Example

Predicting a peak induced potential difference

A magnet dropped from a fixed height through a $150$ turn coil gives a peak induced potential difference of $V0.30\ \text{V}$ .
The coil is replaced by an identical coil of $450$ turns, and the drop height is raised so that the magnet passes the coil at twice the speed.
Tripling the number of turns multiplies the peak value by $3$ , because each turn contributes an equal share.
Doubling the speed multiplies the peak value by a further $2$ , because the field changes in half the time.
The predicted peak is $VV=0.30\times3\times2=1.8\ \text{V}$ .
Dropping the same magnet from the original height through the $450$ turn coil would give $V0.30\times3=0.90\ \text{V}$ , which separates the effect of the turns from the effect of the speed.

Exam technique

Answering a factors question

Name the factor you are changing, state whether it is increased or decreased, then link it to the rate at which the magnetic field through the coil changes.
Finish with the effect on the induced potential difference, since a factor named without an effect earns nothing.
For a comparison of two traces, quote both the height of the peak and the width of the pulse rather than only the height.
Say directly proportional only when the graph is a straight line passing through the origin.
When asked for one change that increases the reading, choose a factor you can justify in a single step, such as adding more turns, rather than a vague answer such as improving the equipment.

Common Mistake

Do not write that a stronger magnet held still gives a larger induced potential difference, because a steady field induces nothing.
Do not confuse the number of turns with the length of wire in a straight conductor, since only turns linking the changing field add up.
Do not give the resistance of the circuit as a factor affecting the induced potential difference, because it affects only the induced current.
Do not describe a pulse below the zero line as a smaller induced potential difference, since it is the same size in the opposite direction.
Do not change the drop height and the coil in the same run, because the effect of each factor then cannot be separated.

Self review

State the quantity that determines the size of an induced potential difference.
List four changes that each increase the peak induced potential difference in a coil and magnet arrangement.
Explain why a coil of $400$ turns gives twice the reading of an identical coil of $200$ turns.
Describe how a pulse on an oscilloscope changes when the magnet passes the coil twice as fast.
Explain why inserting a soft iron core into the coil raises the induced potential difference.

Rate of change of the magnetic field

Definition

Induced potential difference

An induced potential difference is the potential difference produced across the ends of a conductor by a changing magnetic field.

Definition

Induced current

An induced current is the current driven by an induced potential difference when the conductor forms part of a complete circuit.

The size of the induced potential difference is set by the rate at which the magnetic field through the conductor changes, not by the size of the field itself.
A change completed in a shorter time gives a larger induced potential difference, and the same change spread over a longer time gives a smaller one.
Anything that makes the field through the coil change by a larger amount, or change in a shorter time, increases the induced potential difference.
The induced current grows in proportion to the induced potential difference for a fixed circuit resistance, so the same list of factors controls the current reading.
Each factor works by changing either how much the field through the coil changes or how quickly that change happens.

The five controlling factors

Speed of relative movement:
1. Moving the magnet or the coil faster completes the same change in the field in less time, so the rate of change is greater.
2. Doubling the speed roughly doubles the peak induced potential difference for the same magnet and coil.
Number of turns on the coil:
1. Each turn of wire has a potential difference induced across it, and the turns are joined in series, so their contributions add together.
2. A coil of $200$ turns gives about twice the induced potential difference of an otherwise identical coil of $100$ turns.
Strength of the magnetic field:
1. A stronger magnet, or two magnets used together, produces a larger change in the field for the same movement.
2. Slotting a soft iron core into the coil concentrates the field lines through the coil and increases the induced potential difference sharply.
Area of the coil:
1. A coil of larger cross-sectional area has more of the magnetic field passing through it, so the same movement changes the field through it by more.
Orientation of the movement:
1. Moving a wire at right angles to the field lines makes it cut through the greatest number of them and gives the largest induced potential difference.
2. Moving a wire along the field lines makes it cut none of them, so nothing is induced.

Factors that make no difference

The resistance of the external circuit changes the induced current but not the induced potential difference.
The material of the wire changes the resistance of the coil, so it affects the current rather than the induced potential difference.
The length of time for which the magnet is left inside the coil makes no difference once it has stopped moving, because the reading has already fallen to zero.
The absolute position of the magnet matters only through how much the field through the coil changes as it moves.

Practical

Investigating what changes the induced potential difference

Aim: to find how the peak induced potential difference depends on the speed of movement, the number of turns on the coil and the strength of the magnetic field.
Apparatus: two or three coils of known turns such as $100$ , $200$ and $400$ turns, identical bar magnets, a vertical plastic tube of about $m1\ \text{m}$ , a data logger with a voltage sensor set to record at a high sampling rate, soft iron core, retort stand and clamp, metre rule, foam landing pad and connecting leads.
Variables, speed investigation: the drop height above the coil is the independent variable, the peak induced potential difference is the dependent variable, and the same magnet, coil, number of turns and sampling rate are controlled.
Variables, turns investigation: the number of turns on the coil is the independent variable, the peak induced potential difference is the dependent variable, and the drop height, magnet and coil diameter are controlled.
Method, setting up:
- Clamp the plastic tube vertically and slide the coil onto it so that the magnet must fall straight through the middle of the coil.
- Connect the coil to the voltage sensor and set the data logger to record for a short interval at a high sampling rate so the pulse shape is captured.
- Place a foam pad at the bottom of the tube so the magnet is not damaged when it lands.
- Use the metre rule to mark release heights on the tube, measured from the top of the coil.
Method, changing the speed:
- Release the magnet from the lowest marked height without pushing it, and record the peak induced potential difference from the trace.
- Repeat the drop three times from that height and calculate a mean peak value.
- Repeat for at least five increasing release heights, which give increasing speeds at the coil.
- Calculate the speed at the coil for each height using $v=2ghv=\sqrt{2gh}$ so that speed can be plotted rather than height.
Method, changing the number of turns:
- Fix one release height and use it for every coil so the speed at the coil is the same each time.
- Swap the coil for one with a different number of turns, keeping the coil diameter and the magnet the same.
- Take three drops with each coil and record the mean peak induced potential difference.
Method, changing the field strength:
- Repeat one fixed drop with a single magnet, then with two identical magnets held with like poles together to give a stronger field.
- Repeat the fixed drop with a soft iron core inserted into the coil and compare the peak value with the empty coil.
Measurements and processing: tabulate release height, calculated speed, number of turns and the three peak readings with their mean, then plot peak induced potential difference against speed and against number of turns.
Expected pattern: both graphs are straight lines through the origin, the stronger field gives a larger peak at the same speed, and the soft iron core gives the largest increase of all.
Sources of uncertainty: the magnet may tilt or rub inside the tube, the data logger may miss the true peak if the sampling rate is too low, the coil may shift on the tube between runs, and the magnet may lose speed to air resistance.
Improvements: use light gates to measure the actual speed at the coil rather than calculating it, raise the sampling rate until the peak value stops changing, and secure the coil to the tube so it cannot move.
Safety: clamp the tube so it cannot fall, keep magnets away from cards and phones, and stand clear of the base of the tube while a magnet is falling.

Reading the graphs and traces

A straight line through the origin on a graph of peak induced potential difference against speed shows that the two quantities are directly proportional.
A straight line through the origin on a graph of peak induced potential difference against number of turns shows the same proportional relationship for the turns.
Doubling the speed makes the pulse on an oscilloscope twice as tall and half as wide, because the same overall change in the field happens in half the time.
The area under a pulse of induced potential difference against time barely changes when only the speed changes, since the total change in the field is the same.
Reading a value off a straight line through the origin is a matter of scaling, so a coil of triple the turns at double the speed gives six times the original peak.

Example

Predicting a peak induced potential difference

A magnet dropped from a fixed height through a $150$ turn coil gives a peak induced potential difference of $V0.30\ \text{V}$ .
The coil is replaced by an identical coil of $450$ turns, and the drop height is raised so that the magnet passes the coil at twice the speed.
Tripling the number of turns multiplies the peak value by $3$ , because each turn contributes an equal share.
Doubling the speed multiplies the peak value by a further $2$ , because the field changes in half the time.
The predicted peak is $VV=0.30\times3\times2=1.8\ \text{V}$ .
Dropping the same magnet from the original height through the $450$ turn coil would give $V0.30\times3=0.90\ \text{V}$ , which separates the effect of the turns from the effect of the speed.

Exam technique

Answering a factors question

Name the factor you are changing, state whether it is increased or decreased, then link it to the rate at which the magnetic field through the coil changes.
Finish with the effect on the induced potential difference, since a factor named without an effect earns nothing.
For a comparison of two traces, quote both the height of the peak and the width of the pulse rather than only the height.
Say directly proportional only when the graph is a straight line passing through the origin.
When asked for one change that increases the reading, choose a factor you can justify in a single step, such as adding more turns, rather than a vague answer such as improving the equipment.

Common Mistake

Do not write that a stronger magnet held still gives a larger induced potential difference, because a steady field induces nothing.
Do not confuse the number of turns with the length of wire in a straight conductor, since only turns linking the changing field add up.
Do not give the resistance of the circuit as a factor affecting the induced potential difference, because it affects only the induced current.
Do not describe a pulse below the zero line as a smaller induced potential difference, since it is the same size in the opposite direction.
Do not change the drop height and the coil in the same run, because the effect of each factor then cannot be separated.

Self review

State the quantity that determines the size of an induced potential difference.
List four changes that each increase the peak induced potential difference in a coil and magnet arrangement.
Explain why a coil of $400$ turns gives twice the reading of an identical coil of $200$ turns.
Describe how a pulse on an oscilloscope changes when the magnet passes the coil twice as fast.
Explain why inserting a soft iron core into the coil raises the induced potential difference.

13.1.2 Factors affecting the induced potential difference

Rate of change of the magnetic field

The five controlling factors

Factors that make no difference

Investigating what changes the induced potential difference

Reading the graphs and traces

Predicting a peak induced potential difference

Answering a factors question

Review 13.1.2 Factors affecting the induced potential difference by teaching Genie

13.1.2 Factors affecting the induced potential difference

Rate of change of the magnetic field

The five controlling factors

Factors that make no difference

Investigating what changes the induced potential difference

Reading the graphs and traces

Predicting a peak induced potential difference

Answering a factors question

Review 13.1.2 Factors affecting the induced potential difference by teaching Genie

13.1.2 Factors affecting the induced potential difference

Rate of change of the magnetic field

The five controlling factors

Factors that make no difference

Investigating what changes the induced potential difference

Reading the graphs and traces

Predicting a peak induced potential difference

Answering a factors question

Review 13.1.2 Factors affecting the induced potential difference by teaching Genie

13.1.2 Factors affecting the induced potential difference Revision Guide

13.1.2 Factors affecting the induced potential difference

Rate of change of the magnetic field

The five controlling factors

Factors that make no difference

Investigating what changes the induced potential difference

Reading the graphs and traces

Predicting a peak induced potential difference

Answering a factors question

Review 13.1.2 Factors affecting the induced potential difference by teaching Genie

13.1.2 Factors affecting the induced potential difference Revision Guide