4.4 - Motor Effect

A current in a magnetic field experiences a force

• When a current-carrying wire is placed in a magnetic field, the magnetic field around the wire interacts with the magnetic field between the poles.
• The two fields exert a force on each other, causing the wire to move. This is called the motor effect.
• By Newton's third law, the magnet and the wire exert an equal and opposite force on each other.

Factors affecting the force

• Angle:
  • The full force acts when the wire is at 90° (right angles) to the magnetic field.
  • A wire running parallel to the field experiences no force.
  • The force always acts at right angles to both the magnetic field and the current.
• Magnitude - The force increases if the current increases, a stronger magnet is used, or a longer length of wire lies in the field.
• Direction - Reversing either the current or the magnetic field reverses the direction of the force.

Demonstrating the motor effect

• Place a light metal rod across a pair of parallel rails inside a horseshoe magnet to complete a circuit.
• When current flows, the magnetic force pushes the rod so it rolls along the rails.
• The rails and rod are made from a non-magnetic metal (such as aluminium or brass) so they aren't simply attracted to the magnet.

Fleming's left-hand rule

Fleming's left-hand rule finds the direction of the force on a current-carrying conductor in a magnetic field. Hold the thumb, first finger, and second finger of the left hand at right angles to each other:

• The magnetic field always runs from north to south.
• The current is conventional current, which flows from positive to negative.
• Reversing either the current or the field reverses the direction of the force.

Calculating the force on a conductor ($F=BIL$)

The force on a conductor carrying a current at right angles to a magnetic field is calculated using:

Where:

• $F$ = Force, in newtons (N)
• $B$ = Magnetic flux density, in teslas (T)
• $I$ = Current, in amperes (A)
• $L$ = Length of conductor in the field, in metres (m)

Magnetic flux density ($B$) measures the strength of the magnetic field. This equation only applies when the conductor is at 90° to the field lines. If the conductor is parallel to the field, the force is zero.

Worked example - Force on a current-carrying bar

A bar of length 0.25 m carries a current of 12 A. It lies at right angles to a magnetic field of flux density 0.15 T. Calculate the force on the bar.