Question

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

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

Answer 1

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

Magnetic field at the centre of the bigger loop due to flow of current is smaller loop is

$B=\frac{{\mu }_o}{4\pi }\frac{2\pi I{a}^2}{(a^2+x^2{)}^{3/2}}$ (Refer to Image)

$\therefore$ Flux through the bigger loop=

$\Rightarrow \varphi =\overrightarrow{B}\overrightarrow{A}$

$=\frac{{\mu }_o}{4\pi }\frac{2\pi I{a}^2}{(a^2+x^2{)}^3/2}\pi b^2$

$=\frac{{10}^{-7}\times 2\pi \times 2\times (0.3\times {10}^{-2}{)}^2}{\left[\right(0.3\times {10}^{-2}{)}^2+(15\times {10}^{-2}{)}^2{]}^{3/2}}\pi (20\times {10}^{-2}{)}^2$

$\approx 9.11\times {10}^{-11}$ weber .