Use the equation: force on a conductor at right angles to a magnetic field…

The idea

The force on a straight conductor is largest when the conductor sits at right angles to the magnetic field, and it is then given by F = B × I × l. Here B is the magnetic flux density in tesla (T), equivalently newton per ampere metre (N/A m); I is the current in ampere (A); and l is the length of conductor inside the field in metre (m). Check the units: T × A × m gives N, because 1 T = 1 N/(A m). Worked example: a 0.20 m length of wire carries 3.0 A at right angles to a field of flux density 0.50 T, so F = 0.50 × 3.0 × 0.20 = 0.30 N. If the wire lies along the field, the force falls to zero, so the right-angle condition matters.

What earns the marks

• Selects the relationship force = magnetic flux density × current × length for a conductor at right angles to the field.
• Substitutes values in consistent SI units of tesla, ampere and metre before multiplying.
• Calculates the force in newton by multiplying flux density, current and length together.
• Recognises that the force is greatest at right angles to the field and zero when the conductor lies along the field.
• Converts a flux density given in newton per ampere metre to tesla using the equivalence 1 T = 1 N/(A m).

Common mistakes and how to put them right

• Adds the three quantities instead of multiplying them.

  Put it right: Multiply flux density, current and length to obtain the force.

• Uses the length in centimetre without converting to metre.

  Put it right: Divide by 100 so the length is in metre before substituting.

• Treats the force as independent of the angle between wire and field.

  Put it right: State that the full equation applies at right angles and the force is zero when the wire lies along the field.

Exam tips

• Write the equation first, then substitute numbers with their units so the newton result can be checked from T × A × m.
• Convert every length to metre and every current to ampere before multiplying, and keep the flux density in tesla.
• Read the stem for the phrase at right angles; if the wire is described as parallel to the field, the force is zero rather than B × I × l.