Question

Two concentric circular coils, one of small radius $r$ and the other of large radius $R$ are placed co-axially with centers coinciding. If the radius $r$ is changed by $2\%$, then the change in mutual inductance of the arrangement is (Assume $r<<R$ )

• A. $2\%$
• B. $1.5\%$
• C. $4\%$
• D. $0\%$

Answer 1

Answer: (C)

Mutual inductance, $M=\frac{{\mu }_0\pi N_1{N}_2{r}^2}{2R}$
where, $N_1=$ number of turns in inner coil,
$N_2=$ number of turms in outer coil,
$r=$ radius of inner coil
and $R=$ radius of outer coil
$M\propto r^2$
Given that, $\frac{\Delta r}{r}\times 100\%=2\%$
So, by the formula of error analysis
$\frac{\Delta M}{M}\times 100\%=2\left(\frac{\Delta r}{r}\times 100\%\right)$
$=2(2\%)=4\%$