Consider a rectangular loop of sides and carrying a steady current

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

Consider a rectangular loop of sides

a

and

b

carrying a steady current

I

. The loop is placed in a uniform magnetic field

\mathbf{B}

such that the angle between the normal to the plane of the loop and the magnetic field is

\theta

. The loop has

N

identical turns. (i) Show that the forces acting on the pair of opposite sides of length

a

(or

b

) form a couple. (ii) Hence derive an expression for the magnitude of the torque experienced by the loop in terms of

N, I, a, b, B

and

\theta

. (iii) State the values of

\theta

for which the loop is in (1) stable equilibrium and (2) unstable equilibrium, giving reasons for your answer.