Question

The magnets of two suspended coil galvanometers are of the same strength so that they produce identical uniform magnetic fields in the region of the coils. The coil of the first one is in the shape of a square of side a and that of the second one is circular of radius $\frac{a}{\sqrt{\pi }}$ . When the same current is passed through the coils, the ratio of the torque experienced by the first coil to that experienced by the second one is

• A. $1=\frac{1}{\sqrt{\pi }}$
• B. $1:1$
• C. $\pi :1$
• D. $1:\pi$

Answer 1

Answer: (B)

In galvanometer $I\propto \theta =G\theta$
Where, $G=\frac{k}{NAB}$
When coil is in square of shape,
$G=\frac{k}{NAB}=\frac{k}{N{a}^{2}B}\dots$(i)
When coil is in circular shape of radius $a/\sqrt{\pi }$
$G=\frac{k}{NAB}=\frac{k}{N\pi r^2\cdot B}$
$=\frac{k}{N\pi {\left(\frac{a}{\sqrt{\pi }}\right)}^2\cdot B}=\frac{k}{N{a}^{2}B}\dots$ (ii)
So, value of $G$ is same for both type of shape of coil. So, the torque $e=NBIA\sin \theta$ will be same in both the case
$e:e=1:1$