Physics · 4 Electricity and magnetism

4.5.4 Force on a current-carrying conductor

Before you start

Magnetic field lines outside a magnet go from the N pole to the S pole (4.1).
A current in a wire produces a magnetic field around the wire (4.5.3).
Conventional current goes from positive to negative round a circuit, and free electrons move the other way (4.2.2).
Electrons carry a negative charge and protons carry a positive charge; neutrons have no charge (5.1).

Syllabus objectives covered (3)

Describe an experiment to show that a force acts on a current-carrying conductor in a magnetic field, including the effect of reversing: (a) the current (b) the direction of the field
Recall and use the relative directions of force, magnetic field and current
Determine the direction of the force on beams of charged particles in a magnetic field

Part 1 of 6

The experiment: a rod that rolls when the current flows

This subtopic starts with one observation: a wire that carries a current, placed in a magnetic field, has a force on it. This is called the motor effect, because it is what turns an electric motor (4.5.5).
Here is an experiment that shows it. Lay two parallel copper rails flat on the bench. Rest a light copper rod across them, so the rod and rails complete a circuit.
Connect the ends of the rails to a low-voltage d.c. supply, with a switch in series. A variable resistor in series lets you limit the current, because a rod and rails have very little resistance and would otherwise carry a large current and get hot.
Place a U-shaped magnet so that the rod lies between its poles, with one pole above the rod and the other below it. The magnetic field then passes vertically through the rod, at right angles to it.
apparatus diagram — not drawn yet
Two parallel horizontal copper rails with a light copper rod resting across them; the rails connect to a low-voltage d.c. supply through a switch and a variable resistor; a U-shaped magnet straddles the middle of the rod with its N pole above the rod and its S pole below it; an arrow along the rails shows the direction the rod rolls.
The rod is the current-carrying conductor. It sits between the poles, at right angles to the field, and rolls along the rails when the switch closes.
Close the switch. The rod rolls along the rails. Open the switch and the push stops. That is your evidence: the force exists only while there is a current and a magnetic field.
Notice which way the rod moves. It does not move towards either pole. The force is at right angles to the field and at right angles to the rod, which is why the rod rolls along the rails.
The rod is copper, not steel, for a reason. Steel is a magnetic material, so a steel rod would be attracted to the magnet even with the switch open, and you could not tell that effect apart from the force on the current.

Part 2 of 6

Reversing the current, reversing the field

The objective asks for two reversals, and each one has the same result.
Reverse the current. Swap the two connections at the supply. The rod now rolls the opposite way along the rails. The force has reversed.
Reverse the field. Turn the magnet over, so the S pole is above the rod and the N pole below it. The rod again rolls the opposite way. The force has reversed.
Reverse both at once. The two reversals cancel, and the rod rolls in its original direction. This is the trap: two changes do not make 'double the reversal'.
In a written answer, say what moves and which way: 'the rod rolls in the opposite direction'. 'It changes' does not say what changed.
Useful to know, though this objective does not ask for it: a larger current, or a stronger magnet, gives a larger force, so the rod moves off more quickly.

Part 3 of 6

Why there is a force, and when there is none

The current in the rod makes its own magnetic field, in circles around the rod (4.5.3). That field and the magnet's field act on each other.
On one side of the rod the two fields are in the same direction and add, so the combined field is stronger. On the other side they are in opposite directions and partly cancel, so the combined field is weaker. The rod is pushed from the stronger-field side towards the weaker-field side.
This explains the direction. The circular field of the current lies at right angles to the current, so the push is at right angles to both the current and the magnet's field.
It also explains the special case. If the wire lies parallel to the field lines, there is no force at all. The force is largest when the current is at right angles to the field.
So a question that turns the wire to lie along the field from N to S is testing this: the answer is zero force, because the current is parallel to the field.

Part 4 of 6

Fleming's left-hand rule

You need a reliable way to find which way the force acts. Paper 4 gives you nothing to look this up in, so the rule must be recalled.
Hold out your left hand. Point your thumb up, your first finger straight forward, and your second finger out to the side, so that all three are at right angles to each other.
Each finger stands for one quantity. First finger: Field, pointing from N to S. Second finger: Current, pointing the way conventional current flows, from + to −. Thumb: the force, which is the direction of motion.
forces diagram — not drawn yet
A left hand with the thumb pointing up, the first finger pointing forward and the second finger pointing to the side, all three at right angles; the thumb is labelled 'force (motion)', the first finger 'field (N to S)' and the second finger 'current (+ to −)'.
Left hand for the force on a current. First finger = field, second finger = current, thumb = force.
Use it in this order every time. First, find the field direction from the poles: from N to S. Second, find the conventional current direction. Third, turn your hand until the first finger points along the field and the second finger along the current. Then read the force from your thumb.
Do the first two steps on paper before you move your hand. If one finger points the wrong way, the rule gives a wrong answer even though you used it correctly.
Be sure it is the left hand. The right-hand version is a different rule, for the direction of an induced current (4.5.1). Using it here gives the force in exactly the wrong direction.

Part 5 of 6

Reading dots and crosses

Diagrams are flat. When two of the directions lie in the page, the third is at right angles to the page, so it points in or out of it. A symbol shows which.
A dot (⊙) means the current or field comes out of the page, towards you. Think of the point of an arrow coming at you.
A cross (⊗) means the current or field goes into the page, away from you. Think of the feathers at the back of an arrow moving away.
Try one. The field goes from left to right across the page, and the current in a wire goes up the page. Point your first finger to the right and your second finger up the page. Your thumb points into the page, so the force is into the page.
Give your answer in the diagram's own terms: 'into the page', 'towards the top of the page', 'to the left'. A direction such as 'forwards' does not say which way on the diagram.

Part 6 of 6

Beams of charged particles

A current is a flow of charge. So a beam of charged particles moving through a vacuum is a current, even with no wire, and a magnetic field puts a force on it in the same way.
The one extra step is to decide which way the conventional current goes. For positive particles, such as protons or alpha particles, the conventional current is in the same direction as the particles move.
For negative particles, such as electrons or beta particles, the conventional current is in the opposite direction to the way they move. Conventional current is defined as the direction positive charge would move.
So for an electron beam, point your second finger backwards along the beam, against the way the electrons travel. Then use the left-hand rule exactly as before.
It follows that a positive beam and a negative beam, moving the same way in the same field, are pushed in opposite directions. Uncharged particles, such as neutrons, are not a current and are not deflected at all.
forces diagram — not drawn yet
A region of uniform magnetic field into the page shown by a grid of crosses; an electron beam enters from the left moving to the right and curves downwards towards the bottom of the page; a separate beam of positive particles enters from the left and curves upwards towards the top of the page; a dashed straight line shows the undeflected path of an uncharged beam.
Field into the page. Electrons curve one way, positive particles the other, and an uncharged beam goes straight through.
The force is always at right angles to the way the beam is moving, so the beam bends into a curve rather than being pushed sideways in a straight line. The left-hand rule gives the direction of the force at the point where you apply it, such as where the beam enters the field.

Worked examples

Example 1. Describe an experiment to show that a force acts on a current-carrying conductor in a magnetic field. Include what happens when the current is reversed, and when the direction of the field is reversed.

Show the working

Start with the apparatus, because the marks need a conductor, a field and a current. A light copper rod rests across two parallel copper rails, which connect to a low-voltage d.c. supply through a switch.
Place the field correctly: a U-shaped magnet with the rod between its poles, so the field is at right angles to the rod. A rod lying along the field would have no force on it, and the experiment would show nothing.
State the observation, not just the setup. When the switch is closed, the rod rolls along the rails; when the switch is opened, the force stops.
Now the two reversals, each with its own result. Reversing the current (swapping the supply connections) makes the rod roll in the opposite direction.
Reversing the field (turning the magnet over so the poles swap places) also makes the rod roll in the opposite direction.

Answer: A copper rod rests across two copper rails connected to a d.c. supply and switch, with the rod between the poles of a U-shaped magnet and at right angles to the field. When the current flows, the rod rolls along the rails, showing a force acts on it. Reversing the current makes the rod roll the opposite way. Reversing the field (turning the magnet over) also makes it roll the opposite way.

Example 2. A magnet has its N pole at the top of the page and its S pole at the bottom. A straight wire between the poles carries a current into the page. Determine the direction of the force on the wire.

Show the working

Find the field first. Field lines go from N to S, so between these poles the field points down the page.
Find the current. The question says the current goes into the page. On a diagram this is shown by a cross (⊗).
Set your left hand: first finger pointing down the page (field), second finger pointing into the page (current). Keep all three digits at right angles.
Read the thumb. It points to the left.
Check that the answer is at right angles to both the field and the current. Left is at right angles to 'down the page' and to 'into the page', so the answer is at least possible.

Answer: The force on the wire is to the left.

Example 3. A beam of electrons moves from left to right across the page, through a magnetic field directed out of the page. Determine the direction in which the beam is deflected as it enters the field. Then state the direction of deflection for a beam of positive particles moving the same way.

Show the working

Electrons are negative, so the conventional current is opposite to their motion. The electrons move to the right, so the current is to the left.
The field is out of the page (shown by dots).
Left hand: first finger out of the page (field), second finger pointing to the left (current).
Read the thumb. It points towards the top of the page, so the electron beam is deflected upwards.
For positive particles moving to the right, the conventional current is to the right, which is the reverse of the electrons' current. Reversing the current reverses the force, so the positive beam is deflected downwards.

Answer: The electron beam is deflected towards the top of the page. A beam of positive particles moving the same way is deflected towards the bottom of the page.

Where people go wrong

Mistake: Using the right hand to find the direction of the force.

Instead: Use the left hand for the force on a current in a magnetic field.

The right-hand rule is for the induced current in a generator. Swapping hands gives the force in exactly the opposite direction.

Mistake: Pointing the second finger the way the electrons in a beam are moving.

Instead: Point it along the conventional current, which is opposite to the motion of electrons.

The left-hand rule is defined with conventional current. Using the electron direction reverses the answer.

Mistake: Saying that reversing both the current and the field reverses the force.

Instead: Each reversal on its own reverses the force; both together leave it in its original direction.

The second reversal undoes the first, so the two changes cancel.

Mistake: Saying the wire moves towards the N pole or the S pole.

Instead: The force is at right angles to the field, so the wire moves across the field, not along it.

The force comes from the interaction of the wire's own field with the magnet's field. It is not the attraction between a magnet and a magnetic material.

Mistake: Expecting a force on a wire that lies along the field lines.

Instead: A wire parallel to the field has no force on it. The force is largest when the wire is at right angles to the field.

The force acts only when the current is at an angle to the field.

Check yourself

In the rod-and-rails experiment, the current and the magnetic field are both reversed at the same time. Predict the direction in which the rod rolls.
Answer
In its original direction. Each reversal on its own reverses the force, so the two together cancel.
Give one way to reverse the direction of the magnetic field in the rod-and-rails experiment.
Answer
Turn the U-shaped magnet over, so its poles swap places above and below the rod.
In Fleming's left-hand rule, state what the first finger, the second finger and the thumb each represent.
Answer
First finger: magnetic field (N to S). Second finger: conventional current (+ to −). Thumb: force (motion).
A magnetic field is directed into the page. A wire in the field carries a current from left to right across the page. Determine the direction of the force on the wire.
Answer
Towards the top of the page. First finger into the page, second finger to the right, thumb points up the page.
A wire carrying a current lies along the field lines, from the N pole to the S pole. State the size of the force on it.
Answer
Zero. There is no force when the current is parallel to the field.
A beam of electrons moves up the page, through a magnetic field directed out of the page. Determine the direction in which the beam is deflected.
Answer
To the left. The conventional current is down the page (opposite to the electrons); first finger out of the page, second finger down the page, thumb points left.
A beam of protons moves up the page through the same field as in the last question. State the direction in which it is deflected.
Answer
To the right. Protons are positive, so their current is in the opposite direction to the electrons' current, and the force reverses.

Exam questions

Try each part first. Open the mark scheme after you have written your answer.

Question 1. A student rests a light copper rod across two horizontal, parallel copper rails. The rails are connected to a low-voltage d.c. supply through a switch. A U-shaped magnet is placed so that the rod lies between its poles, with the N pole directly above the rod and the S pole directly below it.

(a) State what the student observes when she closes the switch. 1 mark No calculator

Mark scheme

B1 the rod moves / rolls along the rails

(b) State two changes, each of which on its own would make the rod roll in the opposite direction. 2 marks No calculator

Mark scheme

B1 reverse the current / swap the connections to the supply / reverse the battery, owtte
B1 reverse the magnetic field / turn the magnet over so the poles swap places / swap the poles, owtte

(c) The student makes both of the changes in (b) at the same time. Predict the direction in which the rod rolls. 1 mark No calculator

Mark scheme

B1 in the same direction as in (a), owtte

(d) The magnet and supply are back as in the original arrangement. Viewed from above, the rails run from left to right across the page, and the current in the rod flows towards the bottom of the page. Determine the direction in which the rod rolls. 2 marks No calculator

Mark scheme

B1 magnetic field from N to S, i.e. vertically downwards / into the page when viewed from above
B1 rod rolls to the right

(e) Suggest why the student uses a copper rod rather than a steel rod. 1 mark No calculator

Mark scheme

B1 steel is a magnetic material, so it would be attracted to the magnet even with no current, ORA

Question 2. A straight wire runs at right angles to the page, between the poles of a magnet. The N pole is on the left and the S pole is on the right. The current in the wire is directed out of the page.

(a) State the direction of the magnetic field between the poles. 1 mark No calculator

Mark scheme

B1 from left to right / from N to S

(b) Determine the direction of the force on the wire. 1 mark No calculator

Mark scheme

B1 towards the top of the page / upwards; ecf from the field direction in (a)

(c) The wire is turned so that it lies in the plane of the page, running from the N pole to the S pole. The current is unchanged in size. Predict the force on the wire now, and explain your answer. 2 marks No calculator

Mark scheme

B1 no force / the force is zero
B1 because the current is parallel to the magnetic field, owtte

Question 3. In an evacuated tube, a narrow beam of electrons travels from the top of the page towards the bottom. It passes through a region where there is a uniform magnetic field directed into the page.

(a) State the direction of the conventional current that the electron beam represents. 1 mark No calculator

Mark scheme

B1 towards the top of the page / opposite to the direction the electrons move

(b) Determine the direction in which the beam is deflected as it enters the field. 2 marks No calculator

Mark scheme

B1 left-hand rule applied with the current up the page and the field into the page (conventional current opposite to the electron motion)
B1 to the left; ecf from the current direction given in (a)

(c) The electron beam is replaced by a beam of positively charged particles travelling in the same direction. Predict the direction in which this beam is deflected. 1 mark No calculator

Mark scheme

B1 to the right / opposite to the electron beam; ecf from (b)

(d) A beam of neutrons is sent through the same field. Suggest what happens to the beam, and why. 2 marks No calculator

Mark scheme

B1 it is not deflected / it continues in a straight line
B1 neutrons have no charge, so the beam is not a current and there is no force on it

How this is examined

Describing the experiment that shows a force on a current, with both reversals: a three- or four-mark Describe part, which may ask you to complete or label a diagram of the apparatus A conductor (a rod or wire) between the poles of a magnet, at right angles to the field; the conductor in a circuit with a d.c. supply and a switch; the observation that it moves when the current is switched on; reversing the current makes it move the opposite way; reversing the field (turning the magnet over or swapping the poles) makes it move the opposite way.
Finding the direction of the force with Fleming's left-hand rule: a one- or two-mark Determine or State part on a diagram with the poles labelled and the current shown by an arrow, a dot or a cross First finger along the field from N to S; second finger along the conventional current from + to −; the thumb gives the force. The answer stated in the diagram's own terms, such as 'into the page', 'towards the top of the page' or 'to the left'.
Which way a beam of electrons or positive particles is deflected: a one- or two-mark Determine part about a beam crossing a magnetic field in a vacuum tube, which may be followed by a Predict part for a beam of the opposite charge The conventional current taken as opposite to the motion of electrons, and in the direction of motion of positive particles; the left-hand rule applied to that current; the direction of deflection stated. A beam of opposite charge moving the same way is deflected the opposite way; an uncharged beam is not deflected.
What reversing the current, the field or both does to the force: one-mark State or Predict parts that follow on from the experiment Reverse the current or the field alone: the force reverses, so the conductor moves the opposite way. Reverse both: the force is in its original direction. Name what moves and which way, not just 'it changes'.
Why a wire lying along the field has no force on it: a one- or two-mark Predict or Explain part in which the wire is turned to lie along the field No force (zero); because the current is parallel to the magnetic field. The force is largest when the current is at right angles to the field.

Words to know

Motor effect: The force on a current-carrying conductor in a magnetic field. It is the effect that turns an electric motor.
Fleming's left-hand rule: First finger along the field (N to S), second finger along the conventional current (+ to −), all at right angles: the thumb gives the direction of the force.
Conventional current: The direction positive charge would move: from + to − round a circuit, and opposite to the direction electrons move.
Magnetic field direction: The direction of the field lines, from the N pole to the S pole outside a magnet.
Dot and cross: Symbols for a direction at right angles to the page: a dot means out of the page, towards you; a cross means into the page, away from you.

All Physics lessons Next: 4.5.5 The d.c. motor