Question

A circular loop of radius $0.3$ cm lies parallel to a much bigger circular loop of radius $20$ cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is $15$ cm. If a current of $2.0$ A flows through the smaller loop, then the flux linked with bigger loop is :

• A. $3.3\times {10}^{-11}\text{weber}$
• B. $6.6\times {10}^{-9}\text{weber}$
• C. $9.1\times {10}^{-11}\text{weber}$
• D. $6\times {10}^{-11}\text{weber}$

Answer 1

The correct option is C $9.1\times {10}^{-11}\text{weber}$



Let current in bigger loop is $i_2$ and smaller loop is $i_1$
${\varphi }_1$ be flux due to smaller loop at bigger loop
${\varphi }_2$ be flux due to bigger loop at smaller loop
The coefficient of mutual inductance between the loops is
$M=\frac{{\varphi }_1}{i_1}=\frac{{\varphi }_2}{i_2}$
$\frac{{\varphi }_1}{i_1}=\frac{B_{2}A}{i_2}=\frac{{\mu }_0{R}^2\pi r^2}{2(x^2+R^2{)}^{\frac{3}{2}}}$
${\varphi }_1=\frac{{\mu }_0{i}_1{R}^2\pi r^2}{2(x^2+R^2{)}^{\frac{3}{2}}}$

$\therefore {\varphi }_1=\frac{{\mu }_0\times 2\times (20\times {10}^{-2}{)}^2}{2\left[\right(0.02{)}^2+(0.15{)}^2{]}^{\frac{3}{2}}}\times \pi \times (0.3\times {10}^{-2}{)}^2=9.1\times {10}^{-11}\text{wb}$