A wire carries a current of 0.71 A. This wire makes an angle of 46° with respect to a magnetic field of magnitude 6.4 * 10-5 T. The wire experiences a magnetic force of magnitude 8.9 * 10-5 N. What is the length of the wire?

2.72 m.

Explanation:

Using,

F = BiLsin∅ ... Equation 1

Where F = Force on conductor carrying current in a magnetic field, B = magnetic Field, i = current, L = Length, ∅ = angle between the wire and the magnetic field.

make L the subject of the equation

L = F/Bisin∅ ... Equation 2

Given: F = 8.9*10⁻⁵ N, B = 6.4*10⁻⁵ T, i = 0.71 A, ∅ = 46°

Substitute into equation 2

L = 8.9*10⁻⁵ / [6.4*10⁻⁵ * 0.71*sin46°]

L = 8.9/[6.4*0.71*0.72]

L = 8.9/3.272

L = 2.72 m.