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The motor effect and coil turning

Key idea: A current across an external magnetic field produces a force perpendicular to both. Opposite currents on two sides of a coil give opposite forces that can turn it.

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Every electric motor, from a phone’s vibration motor to the motors that drive an MRT train, works because a wire carrying a current in a magnetic field is pushed sideways. One hand rule predicts which way the push acts, and a pair of these pushes on the two sides of a coil makes it turn.

Use conventional current and the dot/cross symbols from magnetic fields made by currents. The dot • means out of the page; the cross × means into the page. The right-hand grip rule finds a current’s own field; the left-hand rule below finds force in an external field.

The force on a current-carrying conductor

A current-carrying conductor placed across an external magnetic field feels a magnetic force. This field is made by another magnet or coil; do not confuse it with the conductor’s own field. This is the motor effect. You can show it, and what reverses it, with a simple experiment.

Showing the force on a current-carrying conductorPanel A is a top view. Two parallel horizontal copper rails are joined at their left ends to a low-voltage D.C. supply through a switch and a rheostat; the positive terminal connects to the top rail. A copper rod rests across the rails between the poles of a magnet, with the N pole above the rails and the S pole below, so the magnetic field points down into the page. Conventional current flows along the top rail, down the rod from the top rail to the bottom rail, and back along the bottom rail. The force on the rod points to the right, along the rails, away from the supply. Panel B is a front view of the same set-up, looking along the rod. The N pole is above and the S pole below, so the field points down the page. The rod is seen end-on with its current coming out of the page. The force on it points to the right.A. Top view, looking downswitch+−D.C. supplyrheostatcopper railsmagnet: N above, S belowIcopper rodF× B into the page: N above, S belowI: top rail → bottom railF: right along the railsB. Front view, along the rodNSBIFB points down, from N to S• I out of the pageF right, as in the top view
Showing the force on a current-carrying conductorPanel A is a top view. Two parallel horizontal copper rails are joined at their left ends to a low-voltage D.C. supply through a switch and a rheostat; the positive terminal connects to the top rail. A copper rod rests across the rails between the poles of a magnet, with the N pole above the rails and the S pole below, so the magnetic field points down into the page. Conventional current flows along the top rail, down the rod from the top rail to the bottom rail, and back along the bottom rail. The force on the rod points to the right, along the rails, away from the supply. Panel B is a front view of the same set-up, looking along the rod. The N pole is above and the S pole below, so the field points down the page. The rod is seen end-on with its current coming out of the page. The force on it points to the right.A. Top view, looking downswitch+−D.C. supplyrheostatcopper railsmagnet: N above, S belowIcopper rodF× B into the page: N above, S belowI: top rail → bottom railF: right along the railsB. Front view, along the rodNSBIFB points down, from N to S• I out of the pageF right, as in the top view
With the switch closed, the rod rolls along the rails. Reversing the current alone, or turning the magnet over alone, makes it roll the other way. Schematic, not to scale.

Apparatus: two parallel bare copper rails, a light bare copper rod resting across them, a strong U-shaped magnet (or two flat magnets on a steel holder), a low-voltage D.C. supply, a switch, a rheostat and connecting leads.

Method:

  1. Connect the supply, switch and rheostat to the ends of the rails, as in the figure.
  2. Place the magnet so the rod lies between its poles, with the N pole above the rails and the S pole below. The field is then vertical, at right angles to the rod.
  3. Close the switch briefly and watch the rod. Open the switch.
  4. Swap the connections at the supply to reverse the current. Close the switch and watch again.
  5. Put the connections back. Turn the magnet over so that the S pole is above, reversing the field. Close the switch and watch.
  6. Reverse both the current and the field. Close the switch and watch.

Use a teacher-approved low-voltage supply and apparatus within their current ratings. Start with the rheostat at high resistance and close the switch only briefly: the rod and rails can heat up. Switch off before changing connections. Low voltage alone does not prevent a large current.

Observations from the rail experiment in the figure
TrialCurrent in the rodMagnetic fieldWhat the rod does
Switch openNoneInto the page (N above)Stays still
1Top rail to bottom railInto the page (N above)Rolls right, away from the supply
2: current reversedBottom rail to top railInto the page (N above)Rolls left
3: field reversedTop rail to bottom railOut of the page (S above)Rolls left
4: both reversedBottom rail to top railOut of the page (S above)Rolls right

Conclusions:

  • A current-carrying conductor in a magnetic field feels a force. With no current, there is no motor-effect force. Gravity and contact forces still act on the rod.
  • The force is at right angles to both the current and the field: the rod rolls along the rails.
  • Reversing the current reverses the force. Reversing the field reverses the force.
  • Reversing both leaves the force in its original direction, because it is reversed twice.

If the conductor lies along the field lines instead of across them, there is no force.

The force arises because the current has its own magnetic field. On one side of the rod this field adds to the magnet’s field and on the other side it opposes it, so the rod is pushed from the stronger field towards the weaker one.

Check your understanding 1 Describe the experiment

Using the figure and observations, describe a teacher-supervised low-voltage experiment to show that a current-carrying conductor in a magnetic field feels a force. State what happens when the current alone, the field alone, or both are reversed.

Show answer

Rest a copper rod across two copper rails joined to a low-voltage D.C. supply through a switch and a rheostat, with the rod between the poles of a U-shaped magnet so that the field is at right angles to the rod. Close the switch only briefly, and switch off before changing the connections or the magnet. When the switch is closed, the rod rolls along the rails. Reversing the current makes it roll the other way; reversing the field instead, by turning the magnet over, also makes it roll the other way. Reversing both makes it roll the original way.

Check your understanding 2 Correct the double-reversal prediction

In the rail experiment the rod rolls right. A student reverses the current and also turns the magnet over:

  1. Reversing the current alone would make the rod roll left.
  2. Turning the magnet over reverses the field, which reverses the force again.
  3. Two changes were made, so the rod rolls left, faster than before.
Which is the first wrong step?
Show answer

The first error is step 3. Current reversal reverses the magnetic force once, and field reversal reverses it again: the original rightward force direction is restored. Equal current and field magnitudes do not justify an increased force, and no extra speed follows from merely reversing them.

Fleming’s left-hand rule

Hold your left hand with the thumb, first finger and second finger all at right angles to each other.

  • First finger: Field, from N to S.
  • Second finger: conventional current.
  • Thumb: the magnetic force on the conductor.

The thumb gives force direction. A conductor free to move from rest starts moving that way; an object already moving need not travel in the force direction.

The rule works when the current and the field are at right angles. It gives the direction of whichever quantity you do not know, as long as you know the other two.

Worked example 1

Checking the rail experiment with the rule

Problem

In the front view of the experiment, the field points down the page and the current in the rod comes out of the page. Find the direction of the force on the rod.

Show full solution

  1. Set the field

    Method

    Point your left first finger down the page.

    Reason

    The field runs from the N pole above to the S pole below.

    Working

    Answer

    First finger: down.

  2. Set the current

    Method

    Turn your hand so the second finger points out of the page, at you.

    Reason

    A dot means current coming out of the page.

    Working

    Answer

    Second finger: out of the page.

  3. Read the thumb

    Working

    Answer

    The thumb points to the right, so the force on the rod is to the right. This matches the rod rolling right in trial 1.

Check your understanding 3 Use two known directions to find the third

“Up”, “down”, “left” and “right” below are directions on the page.

The field points into the page. The current flows to the right. Which way is the force?
The field points out of the page. The current flows up the page. Which way is the force?
The field points to the left. The current flows into the page. Which way is the force?
The field points to the right. The force on a wire is down the page. Which way is the current in the wire?
The current flows to the right. The force is out of the page. Which way does the field point?
A wire carries a current to the right in a field that also points to the right. What is the force on it?
Show answer

With the directions defined on the page: (1) force up, (2) force right, (3) force up, (4) current into the page, and (5) field up. Keep first finger along field, second finger along conventional current and thumb along force. (6) zero magnetic force when current is parallel to the field; perpendicular fingers cannot represent that parallel case.

Check your understanding 4 Correct the finger assignment

A wire carries a current into the page in a field that points up the page. A student finds the force like this:

  1. The field points up the page and the current points into the page.
  2. Left hand: first finger along the current, into the page; second finger along the field, up the page.
  3. The thumb points left, so the force is to the left.
Which is the first wrong step?
Show answer

The first error is step 2: first finger must follow the upward field, and second finger the current into the page. The left thumb then points right, so the magnetic force is rightward. Swapping field and current fingers produces the opposite answer.

Why a current-carrying coil turns

A rectangular coil between the poles of a magnet has two sides that lie across the field. The current flows in opposite directions along these two sides: along one side and back along the other.

Opposite forces turn a current-carrying coilEnd view along the rotation axis of a rectangular coil, with north on the left and south on the right. The active sides are perpendicular to the page. Current is out of the page on the left and into the page on the right. Field points right, so the left force is up and the right force down. At this orientation these forces form a clockwise couple. The two end connections overlap in projection as one horizontal line. The rotation axis is the central point; its dashed line is a label leader. The turning effect changes as the coil rotates.End view along the coil’s rotation axisActive sides perpendicular to the page: • current out, × current in.NSField B →Axis, seen end-onF upF downClockwise hereI out of the pageI into the pageEqual and opposite forces, separated lines of action: a couple.
Opposite forces turn a current-carrying coilEnd view along the rotation axis of a rectangular coil, with north on the left and south on the right. The active sides are perpendicular to the page. Current is out of the page on the left and into the page on the right. Field points right, so the left force is up and the right force down. At this orientation these forces form a clockwise couple. The two end connections overlap in projection as one horizontal line. The rotation axis is the central point; its dashed line is a label leader. The turning effect changes as the coil rotates.End view along the coil’s rotation axisActive sides perpendicular to the page: • current out, × current in.NSField B →Axis, seen end-onF upF downClockwise hereI out of the pageI into the pageEqual and opposite forces, separated lines of action: a couple.
Opposite forces on either side of the axis turn the coil clockwise at this orientation. Dots mean current towards you; crosses away; not to scale.

In the figure, the field points to the right. On the left side the current comes out of the page, and Fleming’s left-hand rule gives an upward force. On the right side the current goes into the page, giving a downward force. The two forces are equal and opposite but act along different lines, one on each side of the axis. Together they make a turning effect, so the coil begins to turn clockwise in this view, at the orientation shown.

A complete explanation has three links:

  1. The current flows in opposite directions in the two sides of the coil.
  2. In the same magnetic field, the two sides feel forces in opposite directions.
  3. The forces act on opposite sides of the axis, so they turn the coil.

The turning effect changes as the coil rotates, so this explains why the coil starts to turn from the position shown.

Check your understanding 5 Predict the turning effect at the shown orientation

In the figure, only the magnetic field is reversed. Which way does the coil turn?
Both the current and the field are reversed. Which way does the coil turn?
Show answer

Reversing only the field reverses both forces: the left side is pushed down and the right side up, giving an anticlockwise turning effect. Reversing both current and field restores the left-up/right-down forces and clockwise turning effect. Use the shown starting orientation to apply the rule.

Check your understanding 6 Test the lines of action at another orientation

View a coil end-on along its rotation axis. The active sides are above and below the axis. The field points right; current comes out of the page above and goes in below. Draw both force arrows on paper. Does each force have a turning effect about the axis? Explain.

Show answer

Fleming’s left-hand rule gives an upward force at the upper side and a downward force at the lower side. The forces are not zero: each current is perpendicular to the field. But both lines of action pass through the central axis, so each has zero perpendicular distance from that axis and produces zero turning effect about it. The equal opposite forces also give zero resultant force. Compare your sketch with a dot above the axis, cross below, field arrow right, and the two outward force arrows on the same vertical line through the axis. Each force acts through the axis, so neither starts the coil turning from rest. The currents give opposite forces; check where their lines of action pass.

Common mistakes

  • Using the right hand to find the force. Fleming’s left-hand rule gives the force; the right-hand grip rule gives the field made by a current.
  • Swapping the fingers. The first finger is the field and the second finger is the conventional current; swapping them reverses the answer.
  • Saying that reversing both the current and the field reverses the force. The two reversals cancel.
  • Saying zero resultant force means zero turning effect. At the shown starting orientation, the two opposite forces have separated lines of action and their turning effects add. At another orientation, check the perpendicular distances from the axis.
  • Expecting a force on a wire that lies along the field lines. There is a force only when the current cuts across the field.

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