A moving coil galvanometer has 100 turns and each turn has an area of 2.0 cm². The magnetic field produced by the magnet is 0.01 T and the deflection in the coil is 0.05 radian when a current of 10 mA is passed through it. The torsional constant of the su

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Solution

Q.
A moving coil galvanometer has 100 turns and each turn has an area of 2.0 cm². The magnetic field produced by the magnet is 0.01 T and the deflection in the coil is 0.05 radian when a current of 10 mA is passed through it. The torsional constant of the suspension wire is $x \times 10^{- 5}$ N-m/rad. The value of $x$ is _____. [2024]

Ans.
(4)    $Given, B = 0.01 T, i = 10 m A, N = 100$

$A = 2 \times 10^{- 4} m^{2} : K = ?$

$τ = K θ$ $\dots (i)$

$τ = B i N A \sin ϕ$    $\dots (i i)$

   $From (i) and (i i), K θ = B i N A \sin 90 °$

   $K = \frac{B i N A}{θ}$

$K = \frac{(0.01) \times (10 \times 10^{- 3} A) \times (100) \times (2 \times 10^{- 4} m^{2})}{(0.05)}$

$K = \frac{2 \times 10^{- 4}}{5} = \frac{20}{5} \times 10^{- 5} = 4 \times 10^{- 5} N - m / rad$

$x = 4$

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