Question

Define mutual inductance and write its SI unit.

A square loop of side ‘a’ carrying a current I₂ is kept at distance x from an infinitely long straight wire carrying a current I₁ as shown in the figure. Obtain the expression for the resultant force acting on the loop.

Answer 1

(a) Mutual inductance equals the magnetic flux associated with a coil when unit current flows in its neighbouring coil.

(b) Force per unit length between two parallel straight conductors

\(\frac{F}{L} = \frac{\mu_0I_1I_2}{2\pi r}\)

Force on the part of the loop which is parallel to infinite straight wire and at a distance x from it

F₁ = \(\frac{\mu_0I_1I_2 a}{2\pi r }\)  (away from the infinite long wire)

Force on the part of the loop which is at a distance (x + a) from it

F₂ = \(\frac{\mu_0I_1I_2 a}{2\pi(x+a)} \)

(towards the infinite long wire)

Net force, F_net = F₁ - F₂

F_net = \(\frac{\mu_0I_1I_2 a^2}{2\pi(x+a)}\)

(away from the infinite straight line)