Question

Electric field is restricted to a circular area of diameter $20cm$ as shown in figure. Magnitude of electric field is increasing at a rate of $200V/(m-s)$, then magnitude of magnetic field at a point $20cm$ from the center of circle is

• A. $0.95\times {10}^{-16}T$
• B. $0.25\times {10}^{-16}T$
• C. $0.55\times {10}^{-16}T$
• D. $0.85\times {10}^{-14}T$

Answer 1

The correct option is C $0.55\times {10}^{-16}T$

Using Maxwell's equations:
$\oint B.dl={\epsilon }_0{\mu }_0\frac{d\varphi }{dt}\Rightarrow B.2\pi r=\frac{1}{C^2}.\frac{dE}{dt}\pi R^{2}B=\frac{R^2}{C^2\times 2r}\frac{dE}{dt}\Rightarrow B=\frac{R^2}{4R{C}^2}\frac{dE}{dt}=\frac{R}{4C^2}\frac{dE}{dt}B=\frac{0.1}{4\times 9\times {10}^{16}}\times 200\Rightarrow B=0.55\times {10}^{-16}T$