Force = magnetic flux density × current × length

The idea

The force on a straight current-carrying conductor at right angles to a uniform magnetic field is calculated using F = B × I × l, where F is force in newtons (N), B is magnetic flux density in tesla (T), I is current in amperes (A) and l is the length of conductor in the field in metres (m). The equation applies when the conductor is perpendicular to the field. If the conductor is at an angle, only the component of length perpendicular to the field contributes, but at GCSE you use the full length when at right angles.

For example: A 0.20 m wire carrying 3.0 A in a 0.50 T field experiences F = 0.50 × 3.0 × 0.20 = 0.30 N. Rearranging allows calculation of B, I or l.

What earns the marks

• Recall and apply the equation force = magnetic flux density × current × length.
• Use the correct units: force in N, magnetic flux density in T, current in A, length in m.
• Rearrange the equation to find magnetic flux density, current or length when required.
• Substitute numerical values correctly and evaluate the force, including appropriate significant figures or decimal places.
• Recognise that the equation applies when the conductor is at right angles to the magnetic field.

Common mistakes and how to put them right

• Using length in centimetres instead of metres.

  Put it right: Convert cm to m by dividing by 100 before substituting.

• Confusing magnetic flux density B with magnetic field strength or using the wrong unit, such as N instead of T.

• Forgetting to rearrange the equation correctly when finding B, I or l, leading to multiplying instead of dividing.

Exam tips

• Write the equation, then substitute values with units before calculating to reduce errors.
• Check that the conductor is at right angles to the field; if not, the simple equation may not apply directly.
• Give the unit with your final answer and round sensibly, matching the precision of the data.