Question

(a) (i) A circular loop of area vector A, carrying a current I is placed in a uniform magnetic field vector B. Write the expression for the torque vector τ acting on it in a vector form. 

(ii) If the loop is free to turn, what would be its orientation of stable equilibrium? Show that in this orientation, the flux of net field (external field + the field produced by the loop) is maximum. 

(b) Find out the expression for the magnetic field due to a long solenoid carrying a current I and having n number of turns per unit length.

Answer 1

(a) (i) Torque acting on the current loop 

(ii) If magnetic moment vector m = I vector A is in the direction ofexternal magnetic field i.e., θ = 0⁰.

(b) On applying Ampere’s circuital law ϕ vector B x vector (dl) = μ₀[Total current]

As no magnetic field exists in direction QR, RS and SP, so