Question

(a) Define the term “self-inductance” of a coil. Wire its SI unit. 

(b) A rectangular loop of sides a and b carrying current I₂ is kept at a distance a from an infinity long straight wire carrying current I₁ as shown in the figure. Obtain an expression for the resultant force acting on the loop.

Answer 1

(a) Self-inductance of a coil is equal to emf induced in coil when the rate of change of current through coil is unity or it is equal the amount of magnetic flux linked with coil when unit current flow through the coil. If current I is flowing through coil in time t and ϕ is the flux linked with coil then

ϕ ∝ I  ⇒ ϕ = LI

where L is self-inductance for unit current, that is, I = 1 and L =ϕ.

The SI unit of self-inductance is henry (H).

(b) Let PQRS be the rectangular loop of side a and b.

It is placed at distance a from infinite long straight wire AB. 

• Current through PQRS = I₂.

• Current through AB = I₁.

• Current through the arm PQ is in same direction as current through the arm AB, so they attract each other. 

• Current through the arm RS is in opposite direction as current through the arm AB, so they repel each other. 

• Also, the force on arm QR and SP is equal and opposite and hence it will cancel each other.

Now, we know the magnetic force between two parallel current-carrying conductor of length L is

where r is the distance between two conductors and L is the length of the conductor. Thus, the force on arm PQ is given as

Force on arm RS is given as

Thus, the resultant force acting on the loop is

This is the resultant force acting on the loop.