Physics · 4 Electricity and magnetism

4.5.3 Magnetic effect of a current

Before you start

Outside a magnet, field lines run from N to S, and the direction of a field at a point is the direction of the force on a N pole there (4.1).
Field lines drawn closer together mean a stronger field (4.1).
Iron filings show the pattern of a field; a plotting compass shows its direction (4.1).
Soft iron is magnetised easily and loses its magnetism as soon as the magnetising field is removed (4.1).
Conventional current flows from the positive terminal to the negative terminal, and the difference between d.c. and a.c. (4.2.2).
$P = I V$ (4.2.5).
Sound comes from a vibrating source; a larger amplitude is louder and a higher frequency is a higher pitch (3.4).

Syllabus objectives covered (5)

Describe the pattern and direction of the magnetic field due to currents in straight wires and in solenoids
Describe an experiment to identify the pattern of the magnetic field (including direction) due to currents in straight wires and in solenoids
Describe how the magnetic effect of a current is used in relays and loudspeakers and give examples of their application
State the qualitative variation of the strength of the magnetic field around straight wires and solenoids
Describe the effect on the magnetic field around straight wires and solenoids of changing the magnitude and direction of the current

Part 1 of 7

The field around a straight wire

Any wire carrying a current has a magnetic field around it. The field exists only while the current flows: switch off and it is gone. This is the magnetic effect of a current.
It is the same kind of field you met with bar magnets. A plotting compass placed in it turns to line up with it, and the direction of the field at a point is the direction the compass's N pole points.
Every direction in this subtopic uses conventional current, from the positive terminal round to the negative. If you use electron flow instead, every direction you work out comes out backwards.
The field lines around a long straight wire are concentric circles centred on the wire. They lie in a plane at right angles to the wire, so a vertical wire has horizontal circles around it.
Notice what this pattern does not have: poles. The lines do not start or end anywhere. Each one is a closed loop round the wire.
To find the direction, use the right-hand grip rule. Imagine gripping the wire in your right hand with your thumb pointing along the conventional current. Your fingers curl round the wire in the direction of the field lines.
On a flat page, a wire running into or out of the page is drawn end-on as a small circle. A cross, $\otimes$ , means the current flows into the page, away from you: you are looking at the tail feathers of an arrow. A dot, $⊙$ , means the current flows out of the page, towards you: the point of the arrow.
Put the grip rule on to those symbols. Current into the page ( $\otimes$ ) gives a clockwise field. Current out of the page ( $⊙$ ) gives an anticlockwise field.
forces diagram — not drawn yet
Two end-on views of a wire side by side. Left: wire marked with a cross (current into the page) surrounded by four concentric circles with clockwise arrowheads. Right: wire marked with a dot (current out of the page) with four concentric circles and anticlockwise arrowheads. In both, the gaps between neighbouring circles get larger moving outwards.
Cross gives clockwise, dot gives anticlockwise, and the circles spread out as you move away from the wire.
The trap here is drawing the lines as straight spokes coming out of the wire. A compass next to the wire points along the circle at its position, not towards the wire or away from it.

Part 2 of 7

How strong the wire's field is, and what the current does to it

The field is strongest close to the wire and gets weaker as you move further away from it.
You show this in a drawing through the spacing of the circles: close together next to the wire, then further and further apart going outwards. Evenly spaced circles would say the field is equally strong everywhere, which is wrong.
Increasing the current makes the field stronger at every point. The pattern stays the same, still concentric circles, but you would draw the lines closer together. Decreasing the current does the opposite.
Reversing the current reverses the direction of the field. Every arrow on every circle flips, and every compass needle round the wire turns through 180°. The shape and the spacing do not change.
Keep the two effects apart in your answers. Changing the size of the current changes only how strong the field is. Changing the direction of the current changes only which way the field points.

Part 3 of 7

The field of a solenoid

A solenoid is a long coil of wire, wound in the shape of a cylinder like a spring. Each turn has its own loop of field round it, and inside the coil the fields of all the turns point the same way, so they add together.
Outside the solenoid, the field has the same shape as the field of a bar magnet: lines come out of one end, curve round the outside and go back in at the other end.
Inside, the lines run straight along the length of the solenoid, parallel to each other and evenly spaced.
So a solenoid has poles, just like a bar magnet. Outside, the field lines leave the N end and enter the S end. Inside, they run from the S end to the N end, which closes each loop.
To find which end is N, use the right-hand grip rule the other way round. Curl the fingers of your right hand round the solenoid in the direction the current flows in the turns. Your thumb points along the field inside the solenoid, towards the N pole.
A second check: look straight at one end of the solenoid. If the current goes round that end anticlockwise, that end is a N pole. If it goes round clockwise, that end is a S pole. 'aNticlockwise is N' is one way to hold on to it.
forces diagram — not drawn yet
A horizontal solenoid drawn side-on with current arrows on the visible turns. Inside: four straight, parallel, evenly spaced field lines running left to right. Outside: curved lines leaving the right-hand end, looping round above and below, and entering the left-hand end, spreading out at the ends. Right-hand end labelled N, left-hand end labelled S. A small end view of the N end beside it shows the current going round anticlockwise.
Bar-magnet shape outside, straight parallel lines inside, and the N end is the one where the current goes anticlockwise as you look at it.
The two rules must agree. If they do not, you have used electron flow in one of them, or your left hand.

Part 4 of 7

How strong the solenoid's field is, and what the current does to it

Inside a long solenoid the field is strong and uniform: the same strength and the same direction at every point away from the ends. That is exactly what straight, parallel, evenly spaced lines mean.
At the ends the lines spread out, so the field there is weaker than in the middle.
Outside the solenoid the field is weaker than inside, and it gets weaker the further you go from the solenoid.
Increasing the current makes the field stronger, inside and outside. The pattern stays the same; you would draw the lines closer together.
Reversing the current reverses the field. The N and S poles swap ends, every arrow flips, and a compass at either end turns round. The pattern itself is unchanged.
One more fact you need for the relay later. Putting a soft iron core inside the solenoid makes its field much stronger. A coil with an iron core like this is an electromagnet.

Part 5 of 7

Showing the field in the laboratory

Set-up for a straight wire. Pass a long straight wire vertically through a hole in the middle of a horizontal piece of card. Connect it to a low-voltage d.c. supply, with an ammeter and a variable resistor so you can set a large current.
apparatus diagram — not drawn yet
A horizontal square card supported on a stand, with a vertical straight wire passing through a hole at its centre. The wire is connected in series with a low-voltage d.c. supply, an ammeter, a variable resistor and a switch. Iron filings form rings on the card around the wire, and four plotting compasses sit on the card at equal distances around the wire.
Filings for the pattern, compasses for the direction.
The pattern. Sprinkle iron filings thinly on the card, switch on and tap the card gently. Each filing becomes a tiny temporary magnet in the field. Tapping lets the filings move past the friction of the card so they can turn and line up with the field. They settle into concentric circles round the wire.
The direction. Iron filings cannot show it, because a filing has no marked N end. Place several plotting compasses on the card around the wire. The N pole of each needle points in the direction of the field at that point. Mark those directions as arrows on your drawing.
Reversing. Swap the connections to the supply. Every compass needle turns round, which shows that the field has reversed direction while the pattern stays the same.
Set-up for a solenoid. Wind the coil so that it passes through holes in the card, with the card lying flat along the axis of the solenoid. Half of each turn is then above the card and half below. The filings show the bar-magnet pattern outside and straight parallel lines inside.
Plotting a line accurately. Place a compass near one end of the solenoid and mark a dot at the point its N pole points to. Move the compass so the other end of its needle sits on that dot, and mark the next dot. Repeat, join the dots, and add an arrow in the direction the N pole pointed.
Two practical points. The current must be large and the compasses close to the wire. Otherwise the Earth's magnetic field, which is always there, is comparable with the field of the wire and the compasses do not line up along the circles. A large current also heats the wire, so switch off between observations.

Part 6 of 7

The relay

A relay is a switch operated by an electromagnet. A current in one circuit switches a second, separate circuit on or off.
The input side is a coil wound on a soft iron core. Next to the core is a soft iron armature on a pivot, held back by a spring. When the armature moves, it pushes a pair of contacts together, and those contacts are part of the second circuit.
circuit diagram — not drawn yet
Two separate circuits. Left: a low-voltage cell, a switch and a relay coil wound on a soft iron core, in series. Right: a mains supply, a heater and a pair of open contacts, in series. A pivoted soft iron armature with a return spring sits next to the core, placed so that when it is pulled towards the core it pushes the contacts together. No wire joins the two circuits.
The only link between the two circuits is the moving armature.
Switching on. When a current flows in the coil, the soft iron core becomes magnetised. It attracts the armature, which pivots and pushes the contacts together. The second circuit is now complete and current flows in it.
Switching off. When the coil current stops, the soft iron core loses its magnetism at once, because soft iron is a temporary magnet. The spring pulls the armature back, the contacts separate and the second circuit is broken.
The two circuits are not connected by any wire. The coil circuit acts on the second circuit only through its magnetic field moving a piece of iron. No current passes from one circuit into the other.
Some relays are built the other way round: the contacts are held together until the coil is switched on, and then they are pulled apart. Read the question's description to see which kind it is.
Why use one. A small current at a low voltage can switch on a large current, often at a high voltage. The person pressing the switch is only connected to the safe low-voltage circuit.
Applications. In a car, turning the key sends a small current through a relay coil, and the relay switches the very large current that the starter motor needs. A sensor circuit, such as one that responds to temperature or to light, can only supply a small current; it can operate a relay that switches on a mains heater or a set of lamps.

Part 7 of 7

The loudspeaker

A loudspeaker turns a changing electric current into sound. It has a coil of wire fixed to a paper or plastic cone. The coil is free to move, and it sits in the strong field of a permanent magnet.
apparatus diagram — not drawn yet
Cross-section of a moving-coil loudspeaker: a permanent magnet at the back with N and S labelled, a coil of wire sitting in the magnet's field, the coil attached to the narrow end of a cone, and two wires from the coil leading to an a.c. signal source. A double-headed arrow shows the cone moving in and out.
Current in the coil, field from the magnet, and the cone moves with the coil.
The signal sent to it is an alternating current. While current flows, the coil has its own magnetic field: the magnetic effect of a current again.
The coil's field interacts with the field of the permanent magnet, so a force acts on the coil.
When the current reverses, the coil's field reverses, and so does the force. The coil is pushed one way, then the other, so the coil and the cone vibrate in and out.
The vibrating cone pushes and pulls on the air in front of it, making compressions and rarefactions. That is a sound wave.
The cone vibrates at the frequency of the current, so the frequency of the current sets the pitch of the sound.
A larger current gives a stronger field round the coil and a larger force, so the cone vibrates with a larger amplitude and the sound is louder. This is the effect of changing the size of the current, from earlier, doing a job.
Applications. Loudspeakers are found in radios, televisions, phones and headphones: anything that turns an electrical signal back into sound.

Worked examples

Example 1. A long straight wire passes vertically through a horizontal card. The conventional current in the wire flows downwards. Four plotting compasses are placed on the card close to the wire: one due north of it, one due east, one due south and one due west. The field of the wire is much stronger than the Earth's field at these points. Determine the direction in which the N pole of each compass needle points.

Show the working

Choose a view to work in. Look down on the card from above, with north at the top of your view. The current flows downwards, away from you, so in this view it is going into the page: $\otimes$ .
Apply the right-hand grip rule: thumb pointing away from you, and your fingers curl clockwise. So, seen from above, the field circles the wire clockwise.
Now move round a clockwise circle. At the top of the view (north of the wire), moving clockwise means moving to the right, which is east.
At the right (east of the wire), clockwise means moving down the view: south. At the bottom (south of the wire), it means moving left: west. At the left (west of the wire), it means moving up: north.
Each compass points along the circle at its own position. None of them points at the wire or directly away from it.

Answer: The compass north of the wire points east, the one east of it points south, the one south of it points west and the one west of it points north: a clockwise pattern seen from above.

Example 2. A long solenoid lies horizontally, with end P on the left and end Q on the right. Looking at end Q from the right, the current in the turns flows anticlockwise. (a) Identify the pole at each end. (b) Deduce the direction a compass needle's N pole points when the compass is placed on the axis just beyond Q, and when it is placed outside the solenoid beside its middle. (c) Predict what changes if the current is reversed and made larger.

Show the working

(a) Use the end rule. The current goes round anticlockwise as you look at Q, so Q is a N pole, and P is therefore a S pole.
Check with the grip rule. Curl your right-hand fingers in the direction of the current; your thumb points along the field inside, towards Q. The thumb points to the N pole, so Q is N. The two rules agree.
(b) Beyond Q on the axis: outside a solenoid, field lines leave the N pole. So the field there points away from Q, to the right, and the compass's N pole points to the right.
Beside the middle, outside: the lines that left Q are curving back round to enter P. So outside the solenoid the field points from Q towards P, to the left. Notice this is the opposite way to the field inside.
(c) Reversing the current reverses the field, so Q becomes S and P becomes N, and both compasses turn round.
Making the current larger makes the field stronger everywhere. The pattern does not change.

Answer: (a) Q is a N pole and P is a S pole. (b) Just beyond Q: to the right, away from the solenoid. Beside the middle: to the left, from Q towards P. (c) The poles swap ends and both compasses point the opposite way; the field is stronger, with the same pattern.

Example 3. In a car, turning the key closes a switch in a circuit that contains the coil of a relay. The contacts of the relay are in the circuit of the starter motor, which needs a very large current. Explain how turning the key starts the motor, and suggest why a relay is used rather than putting the key switch directly into the motor circuit.

Show the working

Start with what the key does: it closes the switch in the coil circuit, so a small current flows in the relay coil.
That current magnetises the soft iron core. The coil and core are now an electromagnet.
The core attracts the soft iron armature. The armature pivots and pushes the contacts together.
The closed contacts complete the starter motor circuit, so the large current flows from the battery through the motor and the motor turns.
Now the 'why'. Only the small coil current passes through the key switch, so the key switch and the wires to it can be small. The thick cable for the large current only has to run between the battery, the relay and the motor.
When the key is turned back, the coil current stops, the core loses its magnetism, the spring pulls the armature away and the motor circuit is broken.

Answer: Turning the key sends a small current through the relay coil, which magnetises the soft iron core. The core attracts the armature, which closes the contacts and completes the motor circuit, so the large current flows and the motor turns. The relay lets a small current through the key switch control the very large motor current, so the key switch and its wiring need not carry the large current.

Example 4. Describe how a loudspeaker produces sound from an alternating current. Then explain what happens to the sound if the size of the alternating current is increased while its frequency stays the same.

Show the working

The coil carries an alternating current, so it has a magnetic field that keeps changing in size and direction.
The coil's field interacts with the field of the permanent magnet, so there is a force on the coil.
Each time the current reverses, the coil's field reverses and so does the force. The coil, and the cone fixed to it, are pushed one way and then the other: they vibrate.
The cone pushes on the air, making compressions and rarefactions: a sound wave with the same frequency as the current.
Now the change. A larger current gives a stronger magnetic field round the coil, so the force on the coil is larger.
A larger force moves the cone further each way, so the amplitude of the vibration is larger and the sound is louder. The frequency of the current has not changed, so the pitch stays the same.

Answer: The alternating current gives the coil a changing magnetic field, which interacts with the permanent magnet's field to produce a force that reverses each time the current reverses. The coil and cone vibrate and push on the air, making sound. A larger current gives a stronger field and a larger force, so the cone vibrates with a larger amplitude: the sound is louder, with the same pitch.

Where people go wrong

Mistake: Drawing the field around a straight wire as straight lines radiating out from the wire, like spokes.

Instead: The field lines are concentric circles centred on the wire.

A compass beside the wire points along the circle at that point, never towards or away from the wire. A field line shows the direction a compass points.

Mistake: Drawing the circles around a wire evenly spaced.

Instead: Draw the gaps between the circles getting larger as you move away from the wire.

Line spacing shows field strength, and the field gets weaker with distance from the wire. Even spacing says the opposite.

Mistake: Using the direction of electron flow, or the left hand, in the grip rule.

Instead: Use your right hand and conventional current, from + to −.

Either slip reverses the answer. Electron flow and conventional current point in opposite directions, so using electron flow with the right hand gives the same wrong answer as using the left hand.

Mistake: Saying iron filings show the direction of the field.

Instead: Iron filings show only the pattern. Plotting compasses show the direction.

A filing lines up with the field but has no marked N end, so it looks the same pointing either way along the line.

Mistake: Thinking the current in a relay's coil flows on into the second circuit.

Instead: The coil circuit and the contact circuit are separate. The coil's only job is to magnetise the core so it pulls the armature and closes the contacts.

That separation is the point of a relay: the low-voltage side, and the person using it, are never connected to the high-voltage side.

Check yourself

Describe the pattern of the magnetic field around a long straight wire carrying a current.
Answer
Concentric circles centred on the wire, in a plane at right angles to the wire.
In an end-on drawing, a wire is marked $⊙$ . Is its magnetic field clockwise or anticlockwise?
Answer
Anticlockwise. $⊙$ means the current comes out of the page towards you; with your right thumb pointing towards you, your fingers curl anticlockwise.
How should the spacing of the circles change as you draw further from a current-carrying wire, and why?
Answer
The circles should get further apart, because the field gets weaker as the distance from the wire increases.
Describe the field lines inside a long solenoid, and state what they tell you about the field there compared with outside.
Answer
Straight, parallel and evenly spaced along the solenoid. The field inside is strong and uniform, and it is stronger than the field outside.
The current in a solenoid is reduced to half and reversed. State two changes to its magnetic field.
Answer
The field becomes weaker, and its direction reverses so the N and S poles swap ends. The pattern stays the same.
Why can iron filings show the pattern of a magnetic field but not its direction, and what is used to show the direction?
Answer
Each filing lines up with the field but has no marked N end, so it looks the same either way along a line. Plotting compasses show the direction: the field points the way the N pole of the needle points.
Give two applications of a relay.
Answer
Any two, for example: switching the large current to a car's starter motor from the small current through the key switch; letting a low-current sensor circuit (temperature or light) switch on a mains heater or lamps.
A relay coil takes a current of $0.040$ A from a $12$ V circuit. Its contacts switch a $230$ V heater that takes $5.0$ A. Calculate the power in each circuit.
Answer
Coil: $P = I V = 0.040 \times 12 = 0.48$ W. Heater: $P = I V = 5.0 \times 230 = 1150$ W ( $1.2$ kW to 2 significant figures). Less than half a watt in the coil controls more than a kilowatt in the heater.

Exam questions

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

Question 1. A student investigates the magnetic field around a long straight wire that carries a current from a d.c. supply.

(a) Describe an experiment the student could do to show the pattern of the magnetic field around the wire and its direction. 4 marks No calculator

Mark scheme

B1 wire passes vertically through a horizontal card and is connected to the d.c. supply (large current)
B1 iron filings sprinkled on the card and the card tapped
B1 filings form concentric circles centred on the wire
B1 plotting compass(es) placed on the card (at different positions round the wire); the direction the N pole of the needle points is the field direction owtte

(b) The current flows downwards through the card. Sketch the magnetic field pattern on the card as seen from above. Show the direction of the field. 3 marks No calculator

Mark scheme

B1 at least three concentric circles centred on the wire
B1 gaps between neighbouring circles increase with distance from the wire
B1 arrows showing a clockwise field, as seen from above

Question 2. A long solenoid is connected to a d.c. supply. Looking at end X of the solenoid, the current in the turns flows clockwise.

(a) Identify the magnetic pole at end X. 1 mark No calculator

Mark scheme

B1 south pole / S

(b) State how the strength of the magnetic field inside the solenoid compares with the strength outside it. State also what the field lines inside the solenoid look like. 2 marks No calculator

Mark scheme

B1 field is stronger inside than outside
B1 lines inside are straight, parallel and evenly spaced / field inside is uniform

(c) The current is reversed and increased. Describe the effect on the magnetic field of the solenoid. 2 marks No calculator

Mark scheme

B1 direction of the field reverses / the poles swap / X becomes a N pole
B1 field becomes stronger (pattern unchanged)

Question 3. A low-voltage circuit contains a switch S and the coil of a relay, wound on a soft iron core. The contacts of the relay are in a separate 230 V circuit containing a heater. When the coil is not magnetised, a spring holds the relay's armature away from the core and the contacts are open.

(a) Explain how closing switch S switches on the heater. 3 marks No calculator

Mark scheme

B1 current in the coil magnetises the (soft iron) core / coil becomes an electromagnet
B1 core attracts the armature
B1 armature moves and closes the contacts, completing the heater circuit

(b) Suggest one advantage of switching the heater on with a relay rather than with a switch in the 230 V circuit. 1 mark No calculator

Mark scheme

B1 any one from: the person using S is connected only to the low-voltage circuit / is not connected to the 230 V supply; a small current in the coil circuit switches the large heater current; the switch and wiring in the control circuit can be thinner / cheaper; the heater can be switched remotely or automatically (e.g. by a sensor circuit) owtte

Question 4. A loudspeaker has a coil fixed to a cone. The coil sits in the field of a permanent magnet. An alternating current flows in the coil.

(a) Describe how the loudspeaker produces sound. 3 marks No calculator

Mark scheme

B1 current in the coil produces a (changing) magnetic field
B1 this interacts with the field of the permanent magnet / a current-carrying coil in a magnetic field experiences a force, giving a force on the coil that reverses when the current reverses
B1 coil and cone vibrate, pushing on the air / producing sound waves

(b) Predict the effect on the sound of increasing the frequency of the alternating current while keeping its size the same. 1 mark No calculator

Mark scheme

B1 higher pitch (cone vibrates at a higher frequency)

How this is examined

Describing the card, iron filings and compass experiment for a wire or a solenoid: a three- or four-mark Describe, for a straight wire or for a solenoid Separate points, each stated plainly: the wire passes vertically through a horizontal card (or the coil passes through the card along its axis) and carries a current from a d.c. supply; iron filings are sprinkled on the card and the card is tapped; the filings form concentric circles round the wire (or the bar-magnet pattern for a solenoid); plotting compasses are placed on the card and the N pole of each needle gives the field direction. Reversing the current and seeing the compasses turn round is a further creditable point.
The chain inside a relay, from coil current to the second circuit switching: a three-mark Explain built on a diagram of a relay joining two circuits; a one-mark Suggest about why the relay is used can follow Each link as its own statement: current flows in the coil; the soft iron core becomes magnetised; it attracts the armature; the armature closes the contacts and completes the second circuit. For the reason: 'a small current switches a large current' or 'the user is not connected to the high-voltage circuit'.
Sketching the field around a wire end-on, with its direction and its spacing: a two- or three-mark Sketch on an end-on view of a wire marked with a dot or a cross Circles centred on the wire, not spokes; gaps between the circles growing outwards; arrows in the right direction, clockwise for $\otimes$ and anticlockwise for $⊙$ .
How a loudspeaker turns an alternating current into sound: a three-mark Describe The a.c. in the coil gives a changing magnetic field; it interacts with the permanent magnet's field, so a force acts on the coil and reverses each time the current reverses; the coil and cone vibrate and push on the air to make sound.
Which end of a solenoid is N, and what changing the current does to the field: a one-mark Identify on a solenoid with the current direction marked, then a one- or two-mark Describe or Predict N is the end where the current goes round anticlockwise as you look at it. Reversing the current: 'the field reverses / the poles swap'. Larger current: 'the field is stronger'; adding 'with the same pattern' shows you know only the strength changed.
Where the field of a wire and of a solenoid is strong and where it is weak: a one- or two-mark State Wire: 'strongest near the wire, weaker further away'. Solenoid: 'strong and uniform inside, weaker outside'. If you describe the inside, say why it is uniform: the lines are parallel and evenly spaced.

Words to know

Magnetic effect of a current: The magnetic field produced around any conductor while a current flows in it.
Right-hand grip rule: For a wire: right thumb along the conventional current, fingers curl in the direction of the field. For a solenoid: fingers curl with the current in the turns, thumb points along the field inside, towards the N pole.
Solenoid: A long coil of wire wound in a cylinder shape. With a current, its field outside has the shape of a bar magnet's field.
Uniform field: A field with the same strength and direction at every point, drawn as straight, parallel, evenly spaced lines.
Plotting compass: A small compass whose needle's N pole points in the direction of the magnetic field where it is placed.
Relay: A switch operated by an electromagnet, so that a current in one circuit switches a separate circuit on or off.
Armature: The pivoted piece of soft iron in a relay that the electromagnet attracts, moving the contacts.
Loudspeaker: A device in which an alternating current in a coil, in the field of a permanent magnet, makes a cone vibrate and produce sound.

All Physics lessons Next: 4.5.4 Force on a current-carrying conductor