Question

(a) Obtain an expression for the mutual inductance between a long straight wire and a square loop of side a as shown in Fig. 6.21.

(b) Now assume that the straight wire carries a current of 50 A and the loop is moved to the right with a constant velocity, v = 10 m/s.

Calculate the induced emf in the loop at the instant when x = 0.2 m.

Take a = 0.1 m and assume that the loop has a large resistance.

Answer 1

(a) Take a small element dy in the loop at a distance y from the long straight wire (as shown in the given figure).

Magnetic flux associated with element

Where,

dA = Area of element dy = a dy

B = Magnetic field at distance y

I = Current in the wire

= Permeability of free space = 4π × 10⁻⁷ T m A⁻¹

y tends from x to .

(b) Emf induced in the loop, e = B’av

Given,

I = 50 A

x = 0.2 m

a = 0.1 m

v = 10 m/s