At equilibrium, the deflection ϕ of a moving coil galvanometer with N turns, area A, current I, in a radial magnetic field B and spring constant k satisfies

1. The magnetic torque on the coil is τ = NIAB (with the radial field design). 2. The restoring spring torque is k·ϕ where k is the torsional constant. 3. At equilibrium, the two torques balance: kϕ = NIAB. 4. Solve for ϕ: ϕ = NIAB/k. Deflection is linear in current. _Source: NCERT Class 12 Physics Ch 4 "Moving Charges and Magnetism", §4.11_