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SPI Physics · Electricity and Magnetism

Magnetic Effects of Current

A current makes a magnetic field around it, a current placed in a magnetic field feels a force (the motor), and a coil turned in a magnetic field makes a current (the generator).

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Why this matters

Five questions in the bank: three EASY, one MODERATE and one HARD. They ask the field inside a solenoid, which pole an anticlockwise current makes, what the forefinger stands for in Fleming's left hand rule, how often a generator's current reverses, and the torque on a coil. Each turns on one rule, so learn which rule goes with which device.

Concept 1 of 3: The magnetic field of a wire, a loop and a solenoid

Every current is surrounded by a magnetic field. Bend the wire into a loop and the field is squeezed through the middle; wind many loops into a long coil (a solenoid) and it behaves just like a bar magnet.

Definition

  • Right hand thumb rule: hold the wire with the thumb along the current; the curled fingers show the direction of the field.
  • Clock rule: look at one face of a loop. If the current flows clockwise, that face is a south pole; if anticlockwise, a north pole.
  • Field lines leave the N pole and enter the S pole outside a magnet, and never cross.
  • A solenoid's field gets stronger with more turns, more current, or a soft iron core (which makes it an electromagnet).
SourceShape of the field lines
Straight wireCircles around the wire, centred on it; weaker farther away
Circular loopCircles near the wire; nearly straight lines at the centre
Solenoid, insideParallel straight lines: the field is uniform
Uniform inside a long solenoid, not circular.
Solenoid, outsideLike a bar magnet: from the N end round to the S end
Bar magnetN to S outside, S to N inside, forming closed loops
Circular lines belong to a straight wire; straight parallel lines to the inside of a solenoid.
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Practice questionEasy

Example 1 · Electricity and Magnetism · Magnetic Effects of Current

Magnetic field inside a solenoid is ____ :-

Calling the field inside a solenoid circular

Circular field lines are around a straight wire. Inside a long solenoid the lines are straight and parallel, so the field is uniform.

Mixing up the clock rule

Seen from a face, clockwise current gives a south pole and anticlockwise gives a north pole.
Drill 1 more on the magnetic field of a wire, a loop and a solenoid

Concept 2 of 3: Force on a current in a magnetic field: the motor

A wire carrying current across a magnetic field is pushed sideways. An electric motor uses this push to keep a coil turning, so it changes electrical energy into motion.

Definition

  • Fleming's left hand rule: stretch the thumb, forefinger and middle finger of the LEFT hand at right angles. Forefinger: field. Middle finger: current. Thumb: force (motion).
  • The force is largest when the current is at right angles to the field, and zero when the current runs along the field.
  • For a wire at right angles to the field: F=BILF = BIL.
  • On a coil of N turns and area A, the turning effect (torque) is τ=NIABsin⁡θ\tau = NIAB\sin\theta, where θ\theta is the angle between the field and the line at right angles to the coil (its normal). If the coil's PLANE makes an angle α\alpha with the field, τ=NIABcos⁡α\tau = NIAB\cos\alpha.
  • In a DC motor a split ring commutator reverses the current in the coil every half turn, so it keeps turning the same way.

Force on a wire and torque on a coil

F=BILτ=NIABsin⁡θF = BIL \qquad \tau = NIAB\sin\theta
  • Bmagnetic field, in tesla
  • Icurrent, in amperes
  • Llength of wire in the field, in metres
  • Nnumber of turns of the coil
  • Aarea of the coil, in square metres
  • θangle between the field and the normal to the coil

Worked example

A wire 0.4 m long carries a current of 5 A at right angles to a magnetic field of 0.2 T. Find the force on it.
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Practice questionEasy

Example 2 · Electricity and Magnetism · Magnetic Effects of Current

In the statement of Fleming's left hand rule. What does the fore finger represent?

Using the right hand for a motor

The LEFT hand rule gives the force on a current, as in a motor. The right hand rule is for the induced current in a generator.

Measuring the angle from the coil's plane

In τ=NIABsin⁡θ\tau = NIAB\sin\theta, θ\theta is measured from the coil's normal. If the plane makes 30∘30^\circ with the field, the normal makes 60∘60^\circ, and sin⁡60∘=cos⁡30∘\sin 60^\circ = \cos 30^\circ.
Drill 1 more on force on a current in a magnetic field: the motor

Concept 3 of 3: Electromagnetic induction and the generator

Run the motor backwards: turn a coil in a magnetic field and a current flows in it. Whenever the magnetic field through a coil changes, a current is induced. This is how power stations make electricity.

Definition

  • Electromagnetic induction (Faraday): a changing magnetic field through a coil, or a coil moving across a field, induces a current.
  • Fleming's right hand rule: thumb along the motion, forefinger along the field, middle finger along the induced current.
  • In an AC generator each side of the coil moves up for half a turn and down for the next half, so the current reverses every half revolution.
FactValue
Energy change in a generatorMechanical energy to electrical energy
Rule for the induced currentFleming's right hand rule
Current reversesOnce every half revolution of the coil
Twice in each full turn, not once.
Rings in an AC generatorSlip rings (current keeps alternating)
Rings in a DC generatorSplit ring commutator (current flows one way)
AC frequency in India50 Hz, so the current changes direction 100 times a second
A motor and a generator are built alike: a coil, a magnet and rings. Only the energy change is reversed.
Practice this conceptself-check · 4 quick reps

The same idea in a practice question:

Practice questionModerate

Example 3 · Electricity and Magnetism · Magnetic Effects of Current

The rectangular coil of copper wires is rotated in a magnetic field. The direction of induced current change once in each

One reversal per turn

The current reverses every HALF revolution, so twice in each full turn. A 50 Hz supply changes direction 100 times a second.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Reference tables (2)

The magnetic field of a wire, a loop and a solenoid5 rows
SourceShape of the field lines
Straight wireCircles around the wire, centred on it; weaker farther away
Circular loopCircles near the wire; nearly straight lines at the centre
Solenoid, insideParallel straight lines: the field is uniform
Uniform inside a long solenoid, not circular.
Solenoid, outsideLike a bar magnet: from the N end round to the S end
Bar magnetN to S outside, S to N inside, forming closed loops
Circular lines belong to a straight wire; straight parallel lines to the inside of a solenoid.
Electromagnetic induction and the generator6 rows
FactValue
Energy change in a generatorMechanical energy to electrical energy
Rule for the induced currentFleming's right hand rule
Current reversesOnce every half revolution of the coil
Twice in each full turn, not once.
Rings in an AC generatorSlip rings (current keeps alternating)
Rings in a DC generatorSplit ring commutator (current flows one way)
AC frequency in India50 Hz, so the current changes direction 100 times a second
A motor and a generator are built alike: a coil, a magnet and rings. Only the energy change is reversed.

Watch out for (5)

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