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Magnetic fields made by currents

Key idea: A current creates a magnetic field: circular around a straight wire and like a bar magnet around a solenoid. Reversing the current reverses the field; increasing it strengthens the field.

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In 1820 Hans Christian Ørsted noticed that a compass needle swung whenever a current flowed in a nearby wire. Every current produces a magnetic field, with no permanent magnet needed. The shape of that field depends on how the wire is arranged, a straight wire or a coil, and one hand rule gives its direction.

Use conventional current. In the external metal-wire circuit of a D.C. supply, it flows from the positive terminal towards the negative terminal, opposite to electron flow. Recall how to draw field-line arrows from magnetic fields and field patterns.

An arrow seen end-on gives two symbols: • is its tip coming towards you, out of the page; × is its tail moving away, into the page.

The magnetic field of a current

A straight wire

  • The field lines are circles centred on the wire, in planes at right angles to it.
  • Right-hand grip rule: grip the wire with your right hand, thumb pointing along the conventional current. Your fingers curl in the direction of the field.
  • The field is strongest close to the wire. Draw the circles further apart as you move out.
The magnetic field around a straight wireTwo end-on views of the same straight wire, at the same current magnitude. Current out of the page is a dot, with anticlockwise concentric circular field lines. Current into the page is a cross, with clockwise circles. The gaps grow away from the wire to represent a weakening field. Reversing current reverses every field arrow without changing the pattern or strength.A. Current out of the pageB. Current into the page• conventional current towards you× conventional current away from youField: anticlockwiseField: clockwiseLarger gaps farther out: weaker field.Same current size: same field strength.
The magnetic field around a straight wireTwo end-on views of the same straight wire, at the same current magnitude. Current out of the page is a dot, with anticlockwise concentric circular field lines. Current into the page is a cross, with clockwise circles. The gaps grow away from the wire to represent a weakening field. Reversing current reverses every field arrow without changing the pattern or strength.A. Current out of the page• conventional current towards youField: anticlockwiseLarger gaps farther out: weaker field.B. Current into the page× conventional current away from youField: clockwiseSame current size: same field strength.
Use your right thumb for conventional current and your curled fingers for field direction. The circles are a schematic field pattern, not paths travelled by charges or a measured scale of field strength.

Worked example 1

Drawing the field of a wire carrying current into the page

Problem

A straight wire is at right angles to the page and carries a current into the page. Draw its magnetic field.

Show full solution

  1. Draw the wire

    Method

    Draw a small circle with a cross in it.

    Reason

    The cross shows current going into the page.

    Working

    Answer

    The wire is seen end-on.

  2. Find the direction

    Method

    Point your right thumb into the page.

    Reason

    The grip rule links the current to the field around it.

    Working

    Answer

    Your fingers curl clockwise as you look at the page.

  3. Draw the circles

    Working

    Answer

    Draw three or four circles centred on the wire, with the gaps between them growing outwards. Put a clockwise arrow on every circle.

Check your understanding 1 Correct the first current-direction error

Electrons flow down a vertical wire, from top to bottom. A student finds the field direction as seen from above:

  1. The current flows down the wire, from top to bottom.
  2. Right-hand grip with the thumb pointing down: seen from above, the fingers curl clockwise.
Which is the first wrong step?
Show answer

The first error is step 1, treating electron flow as conventional current. Electrons go down, so conventional current goes up. Seen from above, that current comes towards the observer; the right-hand grip rule therefore gives an anticlockwise field. Step 2 would describe the different case of conventional current going down.

A solenoid

A solenoid is a long coil of wire. The fields of all its turns add up. Here we use an air-cored solenoid and keep its shape fixed. A soft-iron core can strengthen its field, but the air-cored coil already has this pattern.

  • In the central region of a long solenoid, away from the ends, the field is strong and nearly uniform: straight, parallel, evenly spaced lines.
  • Outside, the field has the same pattern as a bar magnet’s, with an N pole at one end and an S pole at the other.
  • Right-hand grip rule for a solenoid: curl the fingers of your right hand round the turns in the direction of the conventional current. Your thumb points to the N end.
  • Another check: look at one end of the solenoid. If the current goes round anticlockwise, that end is N; if clockwise, it is S.
Magnetic field of a current-carrying solenoidA section through the axis of a solenoid with six turns. In the upper row of wire sections the current comes out of the page (dots); in the lower row it goes into the page (crosses). Inside the solenoid the field lines are straight, parallel, close together and point to the right. They leave the right-hand end, which is the north pole, loop round outside above and below the coil, and enter the left-hand end, which is the south pole. One line runs straight along the axis, pointing right both inside and outside the coil. Outside, the pattern matches that of a bar magnet. Curl your fingers with the current; your thumb points towards the north pole.Long air-cored solenoid: section through its axisLeft end: SRight end: N• upper turn sections: current out× lower turn sections: current inInside: field from S to N.Outside: returns from N to S.Nearly uniform inside, away from the ends; schematic, not to scale.
Magnetic field of a current-carrying solenoidA section through the axis of a solenoid with six turns. In the upper row of wire sections the current comes out of the page (dots); in the lower row it goes into the page (crosses). Inside the solenoid the field lines are straight, parallel, close together and point to the right. They leave the right-hand end, which is the north pole, loop round outside above and below the coil, and enter the left-hand end, which is the south pole. One line runs straight along the axis, pointing right both inside and outside the coil. Outside, the pattern matches that of a bar magnet. Curl your fingers with the current; your thumb points towards the north pole.Long air-cored solenoid: section through its axisLeft end: SRight end: N• upper turn sections: current out× lower turn sections: current inInside: field from S to N.Outside: returns from N to S.Nearly uniform inside, away from the ends; schematic, not to scale.
A long solenoid’s central field is strong and nearly uniform; outside it resembles a bar magnet’s field. Use the right-hand grip rule; not to scale.

To draw a solenoid’s field: draw straight, parallel, evenly spaced lines inside with arrows from the S end to the N end. Then continue each line out of the N end, round the outside and back into the S end, like a bar magnet. Lines never cross.

Check your understanding 2 Reverse the solenoid’s current

The current in every turn of the solenoid in the figure is reversed. Which end is now the N pole?
Which way does the field inside the solenoid now point?
Show answer

Reversing the figure’s conventional current swaps the poles: left becomes N and right becomes S. The internal field now points left, from S to N. The outer field returns from the left N end to the right S end.

Changing the current

For the field produced by the current, keep the wire or air-cored solenoid in the same shape and position. Ignore Earth’s field and other fields in this comparison. Changing the current then changes the field’s strength or direction, while preserving its overall pattern. A magnetic core can behave differently, especially at large currents.

How changing the current changes the magnetic field of a wire or solenoid

Change to the currentField strengthField directionHow to draw it
LargerStronger at the same positionUnchangedSame pattern; draw more closely spaced lines
SmallerWeaker at the same positionUnchangedSame pattern; draw more widely spaced lines
Reversed, same sizeUnchangedReversed; a solenoid’s N and S poles swapSame shape and spacing, every arrow reversed
Larger and reversedStronger at the same positionReversedMore closely spaced lines, every arrow reversed

Use the same drawing convention when comparing line spacing. More closely spaced lines represent a stronger field; adding lines does not change the pattern’s shape.

Keep size and direction separate. Reversing a current does not weaken its field, and a larger current does not turn the field round.

Check your understanding 3 Keep strength and direction separate

The current in a straight wire is doubled without changing its direction. What happens to the field at a point 2 cm from the wire?
The current in a solenoid is reversed but kept the same size. What happens to its field?
Show answer

For the straight wire at the fixed 2 cm position, doubling the current gives a stronger field in the same direction. Reversing a fixed air-cored solenoid’s current without changing its magnitude swaps N and S and reverses its field, with unchanged field strength at the same positions. These compare only the current-produced field under the stated fixed-geometry conditions.

Check your understanding 4 Reduced and reversed

Viewed from its left end, a fixed air-cored solenoid initially carries 2.0 A clockwise. In a second trial it carries 1.0 A anticlockwise. On paper, sketch and label the field in and around the solenoid for both trials. Compare the field strength at the same positions and identify the left-hand pole in each trial. Does the field pattern change shape?

Show answer

The smaller current gives a weaker field at the same positions. Clockwise current viewed from the left makes that end S in the first trial; anticlockwise current makes it N in the second. Self-review both sketches: label the other end N then S, respectively. Inside, draw nearly straight parallel lines S to N; outside, curve them back N to S, without crossings. The arrows reverse and, using the same drawing convention, the smaller-current field has more widely spaced lines. The overall pattern keeps the same shape.

Check your understanding 5 Change the view without changing the wire

Electrons flow down the same vertical straight wire in both observations. Observer A looks down from above; observer B looks up from below. On paper, draw the end-on conventional-current symbol and magnetic-field circles for each observer. Do the opposite clockwise or anticlockwise descriptions imply that the physical current was reversed?

Show answer

Conventional current flows up, opposite to electron flow. For A above the wire it comes out of the page (dot) and gives anticlockwise circles. For B below it goes into the page (cross) and gives clockwise circles. Self-review each sketch: circles share the wire’s centre, every arrow follows that view’s grip-rule direction, and spacing increases farther out. These are opposite views of the same physical current and field, not a reversal of the current.

What happens when a current-carrying wire sits in another magnet’s field is the subject of the motor effect and coil turning.

Common mistakes

  • Using electron flow in the grip rule. Use conventional current, which flows the opposite way.
  • Drawing the circles round a wire evenly spaced. The field weakens with distance, so the gaps grow outwards.
  • Saying a reversed current gives a weaker field. Reversing the current reverses the direction only.
  • Getting the arrows in a solenoid the wrong way round. Inside, the field runs from the S end to the N end.

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