Question

An electric field of $300V/m$ is confined to a circular area $10cm$ in diameter. If the field is increasing at the rate of $20V/m-s$, the magnitude of magnetic field at a point $15cm$ from the centre of the circle will be

• A. $1.85\times {10}^{-15}T$
• B. $1.85\times {10}^{-16}T$
• C. $1.85\times {10}^{-17}T$
• D. $5.55\times {10}^{-18}T$

Answer 1

The correct option is D $5.55\times {10}^{-18}T$

$\begin{array}{c}AreaofelectricfieldA=\pi {\left(\frac{d}{2}\right)}^2\\ changeinelectricflux=changeinelectricfield\times area\\ changeinelectricfluxperunittime\frac{d\varphi }{dt}=20\times 3.14\times 5\times 5\times {10}^{-4}\\ Fromamper{e}^{\prime }smaxwelllaw,\\ \oint \begin{array}{c}\overrightarrow{B}\cdot \overrightarrow{dl}=\mu {\in }_0\frac{d\varphi }{dt}\\ B=\frac{\mu {\in }_0\frac{d\varphi }{dt}}{2\pi r}\\ =\frac{20\times \pi \times 25\times {10}^{-4}}{{\left(3\times {10}^8\right)}^2\times 2\times \pi \times 0.05}=5.55\times {10}^{-18}T\end{array}\end{array}$

Hence,

option $\left(D\right)$ is correct answer.