Full chapter
Electromagnetism
All 5 topics and the revision summary on one page.
01
Magnetic fields from currents
An electric current produces a magnetic field around the conductor. The field's pattern depends on the conductor's shape, while the current affects its strength and direction.
Conventional current follows the direction in which positive charge would flow. In a metal it is opposite to electron motion. A settled compass N end gives the local magnetic field direction.
A straight wire: circular field lines
Look along a straight wire, so that the wire runs perpendicular to the page. Its magnetic field lines form circles centred on the wire in this end view. The field direction at any point is tangent to a circle, rather than pointing radially towards or away from the wire.
- Dot: towards you
- A dot represents an arrow tip coming out of the page towards the reader.
- Cross: away from you
- A cross represents an arrow tail going into the page, away from the reader.
In the wire diagrams these marks label current direction. They are not positive and negative charge signs. Always read the nearby label: a dot or cross can also be used for another quantity perpendicular to the page.
Look along the wire
The central dot means current towards you; the central cross means current away from you. Teal arrows show the field. Each compass's labelled N end follows the local tangent.
Current towards you: anticlockwise field
Current away from you: clockwise field
Keep the viewpoint fixed when comparing directions. The circles represent field lines, not paths travelled by the compasses or by charges around the wire.
If you look from the opposite end of the wire, what appears clockwise changes. State the viewpoint before applying a direction rule.
Predict a compass direction
A compass is just to the right of the wire
For current out of the page, the circular field is anticlockwise, so the local field on the wire's right points up the page.
Reverse the current while keeping the compass and viewpoint fixed. The field becomes clockwise and the compass N end points down the page, assuming the wire's field dominates other fields there.
Increasing current magnitude makes the field stronger at a fixed position for the same wire geometry. Reversing current reverses the field direction. These are separate changes: a stronger current in the original direction does not reverse the field.
Within a consistently drawn pattern, closer field-line spacing can show greater strength qualitatively. The drawn lines do not move faster when current increases, and an arbitrary number of lines is not a numerical field measurement.
A solenoid: the field of a coil
A solenoid is a coil with many turns. The fields due to its turns combine to give a pattern like that of a bar magnet. In the central region of a sufficiently long solenoid, the field is approximately uniform: its lines are nearly parallel and similarly spaced.
Outside, lines leave the solenoid's N end and curve round to its S end. Inside, they return from S towards N, forming continuous loops.
Grip the coil with your right hand, curling your fingers in the conventional-current direction around its turns. Your thumb points towards its north end, along the field inside. Looking directly at one end, anticlockwise current makes that end N; clockwise current makes it S.
Match the winding current to the poles
Brown arrows show conventional current; teal arrows show magnetic field. This projected coil has N on the left and S on the right.
Side view: the near-side current rises
The field returns from S to N inside the coil. Outside, it runs from N to S. The paler wire sections are on the far side of the coil.
Look from the left end
Here the teal dot represents field out of the page. The brown circular arrows represent current around the turns.
This is a qualitative pattern. The turn spacing and the number of drawn field lines do not give a numerical field strength.
Reversing the current swaps the N and S ends and reverses the field throughout the pattern. Increasing the current magnitude strengthens the field when the coil geometry and core remain the same.
A suitable soft-iron core becomes magnetised in the coil's field and strengthens the magnetic effect. It loses much of this induced magnetism when the current is switched off. Its contribution depends on the magnetising field and material.
Investigate the field with a compass
- Use suitable low-voltage equipment. Pass a straight wire through a horizontal card and keep the wire vertical. Looking down at the card gives an end view of the wire.
- With current off, record the compass's background direction. With current on, allow a small compass to settle at several marked positions and draw arrows along its N end.
- Keep the wire, positions and viewpoint fixed. Reverse only the current and compare the new directions. Record the current direction as seen from your chosen view.
- Map a solenoid in the same way, recording its current direction and the compass directions near both ends and along the outside. Compare with the bar-magnet-like pattern.
Keep nearby magnets and magnetic objects away, and use a freely moving compass. The needle responds to the resultant field, including Earth's, so the measured pattern need not match the ideal wire or coil pattern where its field is weak.
To investigate current magnitude, keep the geometry, compass position and background field fixed and record the actual current. A reproducible change in compass deflection can show that the wire's contribution has changed. It does not by itself give a calibrated numerical field strength, and a compass already aligned almost fully with the wire's field may turn very little further.
Stay within the equipment's current ratings and switch off between readings where appropriate to limit heating. Heating or moving the apparatus would change more than the intended variable.
Optional check Viewed end-on, a straight wire initially carries current out of the page. The current is then reversed and increased in magnitude, with the wire unchanged. What happens to its magnetic field?
02
Using electromagnets
An electromagnet uses current to produce a controllable magnetic effect. Switching or changing that current can control the force on a nearby magnetic object.
A current-carrying solenoid produces a magnetic field. Its soft-iron core becomes magnetised and strengthens the effect. Soft iron's low retention helps the effect largely disappear after switch-off.
Pick up a load, then release it
- Current flows through a coil around a suitable soft-iron core.
- The core becomes magnetised and attracts an iron load.
- Switching off removes the main magnetising field. The core loses much of its magnetism, allowing the load to be released.
A suitable steel core can retain more magnetism after switch-off, which may prevent the intended release. Material choice depends on what should happen after the current stops.
A magnetic overcurrent trip
In this simplified circuit breaker, a sensing coil carries the current being monitored. An excessive current produces a stronger magnetic effect, which moves an iron armature and releases a latch. A spring opens the contacts and interrupts the circuit.
An electromagnet trips the monitored circuit
A schematic magnetic overcurrent trip is shown in a simple d.c. loop. The sensing coil and contacts are in the same series path as the load. This is not an RCCB.
1. Normal current: contacts closed
The coil senses the load current because that same current passes through it. The latch keeps the contacts closed against the opening spring.
2. Excessive current releases the latch
Excessive current strengthens the magnetic effect. The armature moves towards the core, releases the latch and lets the spring open the contact arm.
3. The latch holds the circuit open
Opening the contacts also stops current in the coil. The mechanical catch retains the open state; losing magnetism does not immediately reconnect the fault.
Brown arrows: conventional current. Orange arrow: armature movement. Dashed links and the green latch are mechanical. The source, coil, contacts and load form one electrical loop.
- Normal current
- The coil has a magnetic effect, but the armature does not release the closed-position latch under the stated operating conditions. The contacts remain closed.
- Excessive current
- The increased magnetic pull moves the armature enough to release the mechanism. The contacts open, breaking the monitored current path.
- After opening
- Current stops and the electromagnet's pull falls. The mechanism retains the tripped, open state until reset after the fault is addressed; it does not immediately reconnect the fault.
This is a magnetic overcurrent mechanism. A residual-current device detects an imbalance between outgoing and returning currents; that is a different operating principle.
When used to protect a mains circuit, the breaker must disconnect the live connection, as explained in electrical protection. The diagram explains the trip mechanism; no mains experiment is needed.
Follow the cause and effect
Why an excessive current opens the circuit
Larger current gives a stronger magnetic effect in the sensing coil and core. The greater attraction moves the armature, releases the latch and lets the contacts open.
The circuit is then open, so current stops. A retained mechanical trip state is necessary: relying only on magnetic pull would allow the attraction to disappear as soon as the current was interrupted.
Optional check A simplified magnetic circuit breaker trips when a large current makes its core attract an armature. Why does it remain open after the current stops?
03
Magnetic force and its direction
A current-carrying conductor in an external magnetic field can experience a force. To predict its direction, identify the field and conventional current separately.
Across the gap between magnet poles, the field points from N to S. Conventional current is opposite to electron motion in a metal. A dot means out of the page and a cross means into it, for the quantity labelled beside the symbol.
Observe the force on a movable wire
Place a straight, movable conducting segment in the gap of a magnet and connect it to a suitable low-voltage d.c. supply, switch and flexible leads. Arrange the current perpendicular to the field and allow the segment to move in the predicted force direction.
Move a current-carrying wire in a magnetic gap
The upper view separates the wire's rear and front ends. Flexible leads allow its straight section to move. Brown arrows show current, teal arrows field, and purple arrows magnetic force.
Only the magnetic force is marked. Weight and support forces still act. The lower end view represents the same wire, not an extra circuit branch.
- With current off, record the segment's position. Gravity and its supports still act; the magnetic force due to current in the segment is absent.
- Close the switch briefly and observe the movement. In the given geometry, the magnetic force is upward.
- Switch off before changing connections. Reverse the current while leaving the magnet arrangement fixed, then switch on and compare: the magnetic force and resulting initial movement reverse.
- Restore the original current direction. Reverse the magnetic field by exchanging the pole positions, keeping the wire geometry comparable. The magnetic force reverses again.
Keep the support arrangement and current magnitude comparable when comparing directions. Current-induced heating can change wire sag or tension, so observe the controlled initial response and limit heating. A movement demonstrates the effect under these conditions; it is not a calibrated measurement of force magnitude.
Use Fleming's left-hand rule
Hold the thumb, first finger and second finger of your left hand mutually perpendicular:
- First finger: field
- Point it along the magnetic field, from N to S across the gap.
- Second finger: current
- Point it along conventional current in the active conductor.
- Thumb: force
- It gives the magnetic force on that conductor.
The right-hand grip rule finds the field produced by a current. Fleming's left-hand rule finds the relative directions of current, an external field and force. Choose the rule for the relationship you are using.
Keep the viewpoint; change one cause
The dot means current out of the page and the cross means current into it. Teal arrows follow the field from N to S. Purple arrows show force on the wire.
Start: field right, current out
Reverse the current only
Reverse the field only
Reverse both
Reversing either current or field reverses the force. Reversing both restores its original direction. No numerical force is represented by arrow length.
| Current in the wire | Gap field | Initial magnetic-force direction |
|---|---|---|
| Out of the page | Right | Up |
| Into the page | Right | Down |
| Out of the page | Left | Down |
| Into the page | Left | Up |
Compare the first and second rows to isolate current reversal. Compare the first and third to isolate field reversal. The last row changes both and returns to the original force direction.
Find a missing direction
The force is downward and the field is rightward
Put your thumb down and first finger right. The second finger points into the page, so that is the required conventional-current direction.
Alternatively, if current is out of the page and force is upward, those two directions require the field to point right. Any two known perpendicular directions can determine the third.
The examples use perpendicular current and field. If a straight segment's current is parallel or opposite to the field, the magnetic force on that segment is zero in this model. Do not force three non-perpendicular directions into the perpendicular-case hand rule.
Optional check In a fixed front view, a wire carries current out of the page in a magnetic field directed right. Its magnetic force is upward. What is the force direction if both the current and the field are reversed?
A force on a charged-particle beam
A magnetic field can deflect moving charges even when they are not confined to a metal wire. In an appropriate evacuated-tube demonstration, an electron beam produces a spot on a fluorescent screen.
- With the applied magnetic field off, record the spot's reference position.
- Apply a magnetic field perpendicular to the beam's initial motion. The spot shifts, showing that the beam has been deflected.
- Keep the beam conditions and tube position fixed and reverse the field. The spot shifts in the opposite direction relative to the reference.
Do not infer a field effect from changing the beam's settings at the same time. The tube and screen provide evidence of deflection; a drawn curved path is a model of the motion between emission and detection.
For positive charges, conventional current follows their motion. For electrons, it points opposite to their motion. Use that conventional-current direction with Fleming's left-hand rule.
The same initial motion, opposite charges
Both beams initially move right. Crosses mean magnetic field into the page. The amber trace shows motion; the purple arrow shows the force at entry only.
Positive charges: initial force upwards
For positive charges, conventional current follows the beam's motion.
Electrons: initial force downwards
For electrons, conventional current is opposite to the beam's motion.
These are qualitative traces, not measured radii. As a beam turns, the force stays perpendicular to its instantaneous motion; it does not keep one fixed upward or downward direction.
Account for the charge sign
An electron beam moves right
The field is into the page. The electrons' motion is rightward, so the conventional-current direction is leftward. The left-hand rule then gives an initial force downward.
With the same initial motion but the field reversed out of the page, the initial force is upward. A positive beam moving right would deflect the opposite way in each case.
Reversing the motion of the same type of charged particles through the same field reverses the conventional-current direction and hence the initial force. For example, electrons initially moving left through the into-page field experience an initial upward force. A suitable comparison requires a beam arrangement that sends them the opposite way; simply reversing an electron gun's supply does not make the same electrons travel backwards through it.
If both the same-charge beam's initial travel and the field are reversed, the initial force returns to its original direction. Compared with the right-moving electrons in an into-page field, left-moving electrons in an out-of-page field also have an initial downward force.
As a beam curves, its instantaneous direction changes and the magnetic force remains perpendicular to that motion. A force drawn downward at entry does not stay vertically downward everywhere along the path. A beam moving parallel to the magnetic field has no magnetic deflection in this simple model.
Optional check An electron beam initially moves right through a magnetic field directed into the page. What is its initial magnetic deflection in this view?
04
Why a current-carrying coil turns
Opposite sides of a current-carrying coil carry current in opposite directions. In a magnetic field, the forces on those sides can form a pair that turns the coil.
A moment is the turning effect of a force about a pivot or axis. It depends on the force and the perpendicular distance from the axis to the force's line of action. Use Fleming's left-hand rule to find each magnetic force.
Follow the current around one coil
The two active sides are parts of one conducting loop. Current runs along one side and back along the other, so their directions are opposite. View the coil along its axle, with the magnetic field directed right.
Two active sides belong to one connected coil
First trace the current. Then look from the near end along the axle to work out the two forces.
A carries current from far to near. B carries the same current from near to far. The opposite directions are two parts of one circuit.
End view: the forces make a clockwise turning pair
Green arrow: magnetic field. Brown dot/cross: current. Purple arrows: forces. Blue curve: turning sense. The force arrows use one qualitative scale.
Explain the rotation
Field right, left current out, right current in
- For the left side, rightward field and out-of-page current give upward force.
- For the right side, rightward field and into-page current give downward force.
- Upward force on the left gives a clockwise moment about the axle. Downward force on the right also gives a clockwise moment.
- The turning effects add, so the coil tends to turn clockwise in this view.
In the symmetric model, the forces are equal and opposite, so their resultant force is zero. Their lines of action are separated, however, so their moments do not cancel. Zero resultant force does not establish zero turning effect.
Reversing the current with the field fixed reverses both forces and the turning direction at this orientation. Reversing only the field has the same effect. Reversing both preserves the original turning direction.
As the coil turns, the perpendicular distances from the axle to the force lines change. At an orientation where those lines pass through the axle, there is no turning moment from them. Opposite forces produce a turning pair only when their lines of action have the required separation.
Increase the turning effect
- More turns
- Each turn contributes forces on its active sides. More turns increase the combined turning effect when current, field, coil size and orientation are otherwise comparable.
- Greater current
- A greater current gives greater magnetic forces on the active sides and therefore a larger turning effect at the same orientation, with the field and coil unchanged.
State what is kept fixed when comparing. Increasing the number of turns can also change a real coil's resistance and current if the supply arrangement is unchanged. A motor's speed is affected by its load and other operating conditions, so it is not a direct measure of turning effect alone.
The d.c. motor changes the coil's connections at the appropriate positions so that rotation can continue in one sense.
Optional check Viewed along its axle, a coil has its left active side carrying current out of the page and its right side carrying current into the page. The field is rightward. Which explanation is correct?
05
The single-coil d.c. motor
A d.c. motor transfers electrical energy into mechanical motion. Its split-ring commutator reverses current in the physical coil every half-turn so that the magnetic forces keep producing the same sense of rotation.
The two active sides of a coil carry opposite currents and experience opposite forces. As a named side moves to the other side of the axle, its force must reverse to keep the turning sense unchanged.
Connect the supply to a rotating coil
- Two magnetic poles
- They provide the external field across the gap, from N to S.
- Coil and axle
- The current-carrying coil rotates about the axle as its two active sides experience magnetic forces.
- Split-ring commutator
- Two conducting segments, insulated from one another, rotate with the coil. Each is connected to one end of the coil.
- Brushes and d.c. supply
- The brushes remain fixed and make sliding contact with the rotating segments. Their supply polarity stays fixed while each segment changes which brush it touches.
The split ring changes each side's connection every half-turn
A and B name the same physical sides throughout. View from the near, commutator end. The field stays rightwards, the right brush stays positive and the left brush stays negative.
1. Initial orientation
A is on the left: its current comes towards the near end, giving an upward force. B is on the right: its current goes away, giving a downward force. The turning effect is clockwise.
2. A quarter-turn: the switching position
A is above the axle and B below. Their force lines would pass through the axle, giving zero turning effect. The brushes are now at the insulating gaps; in this idealised brief interruption, current is zero. Existing rotation can carry the coil through.
The gaps are centred on this zero-turning orientation. A single stationary coil here is not guaranteed to self-start. The brief loss of contact is an idealised switching interval; it is not a third conducting state. The small bridge in lead B crosses the supply wire without joining it.
3. Half a turn from the start
A has moved to the right and B to the left. Their split-ring segments have exchanged brushes, reversing current in each physical side. The forces still give clockwise turning.
Each labelled split-ring segment stays wired to its physical coil side; the stationary brushes exchange segments as the rotor turns. These are two insulated parts of one split ring, not two complete slip rings. The soft-iron cylinder strengthens the field in the coil and its turning effect in this simple model.
Green: field. Brown: current. Purple: force. Blue: turning or existing rotation. O marks the axle. The lower connection view omits the core and separates the leads to expose the complete electrical path.
Follow one named side through a half-turn
- Initial position: A is left of the axle and carries current out of the page, so its force is up. B is right and carries current into the page, so its force is down. With field right, the pair turns the coil clockwise.
- Intervening zero-turning position: A is above the axle and B below it. The force lines would pass through the axle, giving no moment. In the illustrated commutator, the insulating gaps meet the brushes at this position, so current is briefly interrupted.
- After the half-turn: A is now on the right and B on the left. The segments have exchanged brushes. Current in A is into the page and its force is down; current in B is out of the page and its force is up. The pair still gives clockwise turning.
The external supply polarity and magnetic poles stay fixed. It is the connection of each end of the rotating coil that swaps. Without this swap, the named sides would keep their previous currents after exchanging positions, and the forces would tend to turn the coil back.
The switching positions recur every half-turn. Existing rotation can carry the coil through a zero-turning position and the brief contact gap. A single coil resting exactly at such a position is not guaranteed to self-start.
A split ring has two insulated conducting segments that perform this connection swap. Two separate complete slip rings keep each coil end connected to the same brush and do not provide that half-turn reversal.
Why wind the coil on a soft-iron cylinder?
The soft iron becomes magnetised and strengthens the magnetic field through the coil. With current and other conditions comparable, this increases the magnetic forces and the coil's turning effect.
The core strengthens the magnetic effect; the commutator controls the coil-current reversal. These are different jobs. Neither removes the need for a complete current path through the brushes, segments and coil.
Optional check Initially, physical side A of a motor coil is left of the axle with current out of the page. After a half-turn A is on the right. The field remains rightward. What must the split-ring commutator do to maintain clockwise turning?
Revision summary
Fields from currents
- Straight wire
- Field lines are circles centred on the wire. Right thumb follows conventional current; curled fingers give field direction. In a fixed end view, current out of the page gives anticlockwise field and current into it gives clockwise field.
- Solenoid
- Right-hand fingers follow current around the turns and the thumb points towards N. Anticlockwise current viewed from an end makes that end N. Field is approximately uniform in the central region of a long coil, returning inside from S to N and outside from N to S.
- Change the current
- Greater magnitude gives a stronger field with geometry and core fixed. Reversal reverses the wire's field and swaps a solenoid's poles. Do not confuse strength with direction.
In a compass investigation, fix viewpoint and positions, wait for settling, and compare one change at a time. Record actual current and account for background fields. Compass direction alone is not a calibrated numerical field-strength reading.
Controlled magnetic effects
A coil magnetises a suitable soft-iron core when current flows; low retention helps a lifting device release its load at switch-off. In the magnetic overcurrent-trip model, excessive current increases attraction, moves the armature and releases the latch. Contacts open, current stops, and the trip mechanism retains the open state until reset after the fault is addressed.
Force direction and controlled reversals
For mutually perpendicular directions, Fleming's left hand gives first finger = field, second finger = conventional current, thumb = magnetic force. Any two known directions determine the third.
- Field right, current out of the page: force up.
- Field right, current into the page: force down.
- Field left, current out of the page: force down.
- Field left, current into the page: force up.
In the movable-wire experiment, reverse current alone, then restore it and reverse field alone. Either reverses the magnetic force; reversing both restores it. Keep geometry and supports comparable and limit heating. Current off removes this current-dependent magnetic force, not gravity or support forces. Parallel current and field give no magnetic force in the model.
Charged beams: a perpendicular field shifts an electron beam's fluorescent-screen spot; reversing the field reverses the shift. Conventional current follows positive-charge motion and opposes electron motion. With initial motion right and field into the page, positive charges initially deflect up and electrons down. Reversing field or the motion of the same charge type reverses the initial force; reversing both restores it. The local force changes direction as the path curves.
The coil's turning effect
Viewed along the axle with field right, the left active side carrying current out of the page is forced up; the right side carrying current into the page is forced down. Their separated lines of action give clockwise turning. Equal opposite forces can have zero resultant force and a nonzero combined moment.
Identify both force directions and their distances from the axle. If their lines pass through the axle, their moments about it are zero.
More turns increase the combined turning effect when current, field, coil size and orientation remain comparable. Greater current increases the forces and turning effect with the other conditions fixed.
Sustained rotation in the d.c. motor
The split ring rotates with the coil while the brushes remain fixed. Every half-turn the segments exchange brushes, reversing current in each physical side of the coil. After A moves from left to right, its current changes from out of the page to into it, giving downward force and maintaining clockwise turning in the stated rightward field.
The field poles and external supply polarity stay fixed. Existing rotation carries the coil through the zero-turning/contact-gap position; a stationary single coil there may not self-start. Two complete slip rings do not provide this connection swap.
A soft-iron cylinder strengthens the field through the coil and increases its turning effect under comparable conditions. It has a different role from the commutator.
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