For a moving coil galvanometer, the deflection in the coil is 0.05 rad when a current of 10 mA is passed through it. If the torsional constant of suspension wire is $4.0 \times 10^{-5} \mathrm{Nm} \mathrm{rad}^{-1}$, the magnetic field is 0.01 T and the number of turns in the coil is 200 , the area of each turn ( $\mathrm{in} \mathrm{cm}^{2}$ ) is :

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Current Electricity

For a moving coil galvanometer, the deflection in the coil is 0.05 rad when a current of 10 mA is passed through it. If the torsional constant of suspension wire is

4.0 \times 1 0^{- 5} Nm rad^{- 1}

, the magnetic field is 0.01 T and the number of turns in the coil is 200 , the area of each turn (

in cm^{2}

) is :

(A)2.0
(B)1.0✓ Correct
(C)1.5
(D)0.5

Answer: (B)

Solution

At a steady deflection the magnetic torque on the coil balances the restoring torque of the suspension, so

N i A B = K θ

. The area of each turn is

A = \frac{K θ}{N i B} = \frac{( 4.0 \times 1 0 ^{- 5} ) ( 0.05 )}{( 200 ) ( 10 \times 1 0 ^{- 3} ) ( 0.01 )} = 1 \times 1 0^{- 4} m^{2}

. Converted to the units asked, each turn has an area of

1.0 cm^{2}

JEE Main · 2023 · 25 Jan 2023 · Shift 2 · Single correct option

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