Correct Answer - Option 4 : 10
-3
Concept:
Moment of the deflecting couple:
The moment of the deflecting couple = nBIA
When the coil deflects, the suspension wire is twisted. On account of elasticity, a restoring couple is set up in the wire. This couple is proportional to the twist.
If θ is the angular twist, then, the moment of the restoring couple = Cθ, where C is the restoring couple per unit twist.
At equilibrium, Deflecting couple = Restoring couple
Hence we can write, nBIA = Cθ
Calculation:
Given, Number of turns, N = 175
Area = 1 cm-2 = 10-4 m
Torsional constant, C = 10-6 N-m/rad
Current, I = 1 mA = 10-3 A
Torque is given by,
\(\tau = \vec M \times \vec B\)
On substituting the values in Cθ = NBiA, we get
\({10^{ - 6}}\left( {\frac{\pi }{{180}}} \right) = 175 \times B\left( {{{10}^{ - 3}}} \right) \times {10^{ - 4}}\)
\(B = \frac{{{{10}^{ - 6}} \times \pi }}{{180 \times 175 \times {{10}^{ - 3}} \times {{10}^{ - 4}}}}\)
\(B = \frac{{22}}{7} \times \frac{{10}}{{180 \times 175}} \approx 0.001 \approx 1 \times {10^{ - 3}}\)
∴ B ≈ 10-3 T
Thus, the value of B (in Tesla) approximately is 10
-3 T.
