A small circular loop of area A and resistance R is fixed on a horizontal x y -plane with the center of the loop always on the axis n ^ of a long solenoid. The solenoid has m turns per unit length and carries current I counter clockwise as shown in the figure. The magnetic field due to the solenoid is in n ^ direction. List-I gives time dependences of n ^ in terms of a constant angular frequency ω . List-II gives the

Step-by-step solution

Note: This question was given bonus by JEE council. The magnetic field in a solenoid is given by, B → = μ 0 m I n ^ . Therefore, the flux through the loop will be, ϕ = A k ^ · μ 0 m I n ^ For case I: ϕ = B A 2 cos ω t The emf will be, ε = B A ω 2 sin ω t Therefore, the current in the loop will be, i = B A ω 2 R sin ω t The magnetic moment of the loop will be, m → = i A k ^ = B A 2 ω 2 R sin ω t k ^ Therefore, the torque τ → = m → × B → = B 2 A 2 ω 2 R sin ω t k ^ × n ^ ⇒ τ → = - B 2 A 2 ω 2 R i ^ sin 2 ω t ⇒ τ → =