A moving coil galvanometer experience torque `=ki`, where i is current. If N coils of area A each and moment of inertia I is kept in magnetic field B.
(i) If for current `i` deflection is `(pi)/2`, the torsional constant of spring is `(x BiNA)/(pi)`. Find `x^2`
(ii) If a charge Q is passed suddenly through the galvanometer, the maximum angle of deflection is `Qsqrt((BNpiA)/(xI))`. Find `x^2`

Answer

(i) 2
(ii) 2

Explanation

(i) 2 (ii) 2
(i) `tau=k.theta=BiNa:.k=(2BiNa)/(pi) ` (as `theta=pi//2)` (ii) `tau=BiNA`
or `int_(0)^(t) taudt=BNA int_(0)^(t)idt, I omega =BNAQ`, or `omega=(BNAQ)/I`
At maximum deflection, whole kinetic energy (rotational) will be converted into potential energy of spring.
Hence `1/2 I omega^(2)=1/2 k theta_("max")^(2),` Substituting the values the values we get `, theta_("max")=Qsqrt((BNpiA)/(2I))`