A moving coil galvanometer has a coil with 175 turns and area $1 \mathrm{~cm}^{2}$ It uses a torsion band of torsion constant $10^{-6} \mathrm{~N}-\mathrm{m} / \mathrm{rad}$. The coil is placed in a magnetic field B parallel to its plane. The coil deflects by $1^{0}$ for a current of 1 mA . The value of B (in Tesla) is approximately:-

JEE Main · 2019 · 09 Apr 2019 · Shift 2 · Magnetic Effects of Current

A moving coil galvanometer has a coil with 175 turns and area

1 cm^{2}

It uses a torsion band of torsion constant

1 0^{- 6} N - m / rad

. The coil is placed in a magnetic field B parallel to its plane. The coil deflects by

1^{0}

for a current of 1 mA . The value of B (in Tesla) is approximately:-

Answer: (A)

The coil settles where the magnetic torque on it balances the restoring torque of the suspension,

N i A B = C θ

. With

N = 175

i = 1 0^{- 3}

A = 1 cm^{2} = 1 0^{- 4} m^{2}

C = 1 0^{- 6}

N\,m/rad and

θ = 1^{\circ} = \frac{π}{180}

rad, solve for the field:

B = \frac{C θ}{N i A} = \frac{1 0 ^{- 6} \times ( π /180 )}{175 \times 1 0 ^{- 3} \times 1 0 ^{- 4}}

. The numerator is about

1.75 \times 1 0^{- 8}

and the denominator about

1.75 \times 1 0^{- 5}

, so

B \approx 1 0^{- 3}

JEE Main · 2019 · 09 Apr 2019 · Shift 2 · Single correct option