Torque on a Current-loop: Moving-Coil Galvanometer

When the plane of the coil is parallel to the magnetic field

Step 1: Torque formula: τ = NIAB sinθ, where θ is the angle between the normal to the coil and B. Step 2: Torque is maximum when sinθ is maximum, i.e., sinθ = 1, which means θ = 90°. Step 3: When θ = 90°, the normal to the coil is perpendicular to B, which means the PLANE of the coil is PARALLEL to B. Step 4: So τ_max = NIAB. Step 5: When the plane is perpendicular to B (θ = 0°), torque = 0. Many students confuse 'plane of coil' with 'normal to coil', so be careful with options A and B.

The deflecting torque is always NIAB, making deflection directly proportional to current

Step 1: In a normal uniform field, torque = NIAB sinθ, so deflection φ is proportional to φ/sinθ — not a simple linear relationship. Step 2: In a radial field, the plane of the coil always remains parallel to the field lines in every position (θ = 90°, sinθ = 1 always). Step 3: So deflecting torque is always NIAB, regardless of the angle of deflection. Step 4: At equilibrium: NIAB = cφ, giving I = (c/NAB)φ, i.e., I ∝ φ. Step 5: This linear relationship allows the scale to be uniform, making the galvanometer easy to read. Options A, C, D are all wrong — radial field has no effect on these.

cφ

Step 1: When the coil rotates by angle φ (in radians), the suspension strip or spring twists by the same angle φ. Step 2: By Hooke's law for torsion, the restoring torque is directly proportional to the angle of twist. Step 3: Restoring torque = c × φ, where c is the torsional constant (restoring torque per unit angle of twist). Step 4: At equilibrium: Deflecting torque = Restoring torque → NIAB = cφ. Step 5: From this, I = (c/NAB) × φ, giving the linear relationship between current and deflection. Option A (c/φ) has wrong relationship, C and D are dimensionally or conceptually incorrect.

The deflection produced per unit current flowing through it

Step 1: Sensitivity means how much the instrument responds to a small input. Step 2: Current sensitivity = φ/I (deflection per unit current). Step 3: From the galvanometer equation NIAB = cφ, we get φ/I = NAB/c. Step 4: A higher value of φ/I means a larger deflection for the same current — more sensitive. Step 5: Option C describes the 'figure of merit', which is the RECIPROCAL of current sensitivity (I/φ). Option A is the range, and option D is just the coil resistance.