A long solenoid is carrying a current I=I₀ ( t) , having N turns per unit length and radius R . A square loop is placed inside the solenoid with its plane perpendicular to the solenoid axis, and its corners touching the solenoid. Now the emf induced in the square coil.

Step-by-step solution

Given, I=I₀ t Magnetic field inside the solenoid, B= ₀ N I B= ₀ N I₀ t When side of square loop be l , then array rlrl & & 4 l & =2 R & l & = R 2 array Area of square loop, A=l^2 = ( R 2 )^2= ^2 R^2 4 Magnetic flux linked with square loop, aligned & =B A & = ₀ N I₀ t ^2 R^2 4 & = ₀ ^2 R^2 N I₀ t 4 aligned Induced emf in the square coil, e= d d t aligned & = d d t ₀ ^2 R^2 N I₀ t 4 & = ₀ ^2 R^2 N I₀ t 4 ( ^2 4 =246 ) & =2,46 ₀ R^2 N I₀ t aligned Which is closest to the value given in option (c).