Question

In a moving coil galvanometer of coil of $N$-turns of area $A$ have a spring of stiffness $k$.
If coil is deflected by some angle $\phi$ due to flow of $I$ current in uniform radial magnetic field $B$, then

• A. $\phi=\left(\frac{N A B}{k}\right) I$
• B. $\phi=\left(\frac{k}{B N A}\right) I$
• C. $\phi=\left(\frac{k A}{B N}\right) I$
• D. $\phi=\left(\frac{B N}{k A}\right) I$

Answer 1

Answer: (A)

When a current flows through the coil, a torque acts on it. This torque is given by $\tau=N I A B$
where, the symbols have their usual meaning.
Since, the field is radial by design, we have taken $\sin \theta=1$ in the above expression for the torque. The magnetic torque NIAB tends to rotate the coil.
A spring $S_{P}$ provides a counter torque $k \phi$ that balances the magnetic torque $N I A B$; resulting in a steady angular deflection $\phi$. In equilibrium $k \phi=N I A B$
where, $k$ is the torsional constant of the spring, i.e., the restoring torque per unit twist. The deflection $\phi$ is indicated on the scale by a pointer attached to the spring. We have
$\phi=\left(\frac{N A B}{k}\right) I$