Question

(a) Define mutual inductance and write its SI unit. 

(b) A square loop of side a carrying a current I₂ is kept as distance x from an infinity 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 of two coils is equal to the emf induced in one coil when the rate of change of the current through the other coil is unity or it is equal to the amount of magnetic flux linked with one coil when unit current flow through the other coil. If I is the current flowing through one coil and ϕ is the flux linked with other coil, then

ϕ ∝ I or ϕ = MI,

where M is mutual inductance. For unity current, that is, I = L, we get

M = ϕ

The SI unit of mutual inductance is henry (H).

(b) let us consider PQRS is square loop of side a. The loop is placed at distance x from infinite long straight wire AB.

• Current through PQRS = I₂ 

• Current through AB = I₁

Now, the current passing through the arm PQ is in opposite direction of the current passing through AB; hence, they repel each other. The current passing through the arm RS is in the same direction as the current through arm AB, so, they attract each other.

Also, the force on arm QR and SP are equal and opposite to each other and hence they get canceled. Now, the magnetic force between two parallel current-carrying conductor of length L is

Thus, the force on area PQ is given as

Given: The length of PQ = a. Therefore,

Force on the arm RS is given as

Resultant force is

The resultant force acting on loop is