Question Detail
Question
A galvanometer has a spring constant 'k', a magnetic field 'B' and deflection angle θ. The coil has N turns and an area A. Which of the following is the condition for equilibrium of the coil when current I flows in the galvanometer?
Correct Answer
Option B is the correct answer.
Detailed Explanation
In a galvanometer, when current flows through the coil in a magnetic field, it experiences a deflecting torque. This torque is balanced by a restoring torque provided by the spring. At equilibrium, these two torques are equal.The deflecting torque (τ_deflecting) on a current loop in a magnetic field is given by τ_deflecting = NIAB (assuming the field is radial and perpendicular to the coil sides, so sin(θ) = 1).The restoring torque (τ_restoring) of the spring is proportional to the deflection angle (θ) and the spring constant (k): τ_restoring = kθ.At equilibrium: τ_restoring = τ_deflectingkθ = NIAB (often written as kθ = BIAN).
Hint
Equate the restoring torque of the spring (kθ) to the magnetic torque on the coil (NIAB).