A moving coil galvanometer has 200 turns and each turn has an area of 3.0 cm2. The magnetic field inside the galvanometer is 0.02 T. The deflection in the coil is 0.05 rad when a current of 20 mA is passed through it. The torsional constant of the suspension wire will be
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 4.8 x 10−4 Nm rad−1
At steady deflection the magnetic torque on the coil in the radial field is balanced by the restoring torque of the suspension wire.
\( \displaystyle k\phi = NIAB \)
\( \displaystyle k = \frac{NIAB}{\phi} \)
\( N = 200 \)
\( I = 20\,\mathrm{mA} = 2\times10^{-2}\,\mathrm{A} \)
\( A = 3.0\,\mathrm{cm^{2}} = 3.0\times10^{-4}\,\mathrm{m^{2}} \)
\( B = 0.02\,\mathrm{T} \)
\( \phi = 0.05\,\mathrm{rad} \)
\( \displaystyle k = \frac{200\times(2\times10^{-2}\,\mathrm{A})\times(3.0\times10^{-4}\,\mathrm{m^{2}})\times(0.02\,\mathrm{T})}{0.05\,\mathrm{rad}} \)
\( \displaystyle k = \frac{2.4\times10^{-5}\,\mathrm{N\,m}}{0.05\,\mathrm{rad}} \)
\( \displaystyle k = 4.8\times10^{-4}\,\mathrm{N\,m\,rad^{-1}} \)