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, $M=\frac{\mu_{0} \pi N_{1} N_{2} r^{2}}{2 R}$
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
$\frac{\Delta M}{M} \times 100 \%=2\left(\frac{\Delta r}{r} \times 100 \%\right)$
$=2(2 \%)=4 \%$