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 $\varphi$ due to flow of $I$ current in uniform radial magnetic field $B$, then

• A. $\varphi =\left(\frac{NAB}{k}\right)I$
• B. $\varphi =\left(\frac{k}{BNA}\right)I$
• C. $\varphi =\left(\frac{kA}{BN}\right)I$
• D. $\varphi =\left(\frac{BN}{kA}\right)I$

Answer 1

Answer: (A)

When a current flows through the coil, a torque acts on it. This torque is given by $\tau =NIAB$
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 $k\varphi$ that balances the magnetic torque $NIAB$; resulting in a steady angular deflection $\varphi$. In equilibrium $k\varphi =NIAB$
where, $k$ is the torsional constant of the spring, i.e., the restoring torque per unit twist. The deflection $\varphi$ is indicated on the scale by a pointer attached to the spring. We have
$\varphi =\left(\frac{NAB}{k}\right)I$