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# In a moving coil galvanometer, torque on the coil the wire can be expressed as τ = ki , where i is current through the wire and k is constant. The rectangular coil of the galvanometer having number of turns. N, area A and moment of inertia I is placed in magnetic field B. Find . (a) k in terms of given parameters N, I, A and B(b) the torsion constant of the spring, if a current i­0 produces a deflection of π / 2 in the coil.(c) the maximum angle through which the coil is deflected, if charge Q is passed through the coil almost instantaneously. (ignore the damping in mechanical oscillations)

Deepak Patra
6 years ago
Hello Student,
a) The torque acting on a rectangular coil placed in a uniform magnetic field is given by,$\underset{t}{\rightarrow}$
But M = N i A and θ = 90° (for moving coil galvanometer)
∴ τ = N i A B sin 90°
⇒ τ = N i A B
But τ = k i (given)
∴ k i = NiAB
⇒ k = NAB
(b) The torsion constant is given by
C = τ / θ = NiAB /θ
Here given that when i = i0, θ = π / 2
∴ C = 2N i0 AB / π ….(i)
(c) We know that angular Impulse
= NAB
= NABQ …(ii)
This angular impulse creates an angular momentum
…(iii)
From (ii) and (iii)
I ω = NAB BQ ⇒ ω = NABQ / I
This is the instantaneous angular momentum due to which the coil starts rotating. Let us apply the law of energy conservation to find the angle of rotation.
Rotational kinetic of coil
= 1 / 2 I N2 A2 B2 Q2 / I = N2 A2 B2 Q2 / 2I
1/ 2 Cθ2max = N2 A2 B2 Q2 / 2I
⇒ θ2max = N2 A2 B2 Q2 / CI = N2 A2 B2 Q2 / 2Ni0 ABI x π
⇒ θ2max = πNABQ2 / 2i0I ⇒ θ2max = Q √NABπ / 2Ii0
Thanks
Deepak patra