Question

An expression for the magnetic field strength $B$ at the point between the capacitor plates indicates in figure express $B$ in terms of the rate of change of the electric field strength i.e., $dE/dt$ between the plates

• A. $\frac{{\mu }_{0}i}{2\pi r}$
• B. $\frac{{\epsilon }_0{\mu }_{0}r}{2}dE/dt$
• C. zero
• D. $\frac{{\mu }_{0}i}{2\pi }$

Answer 1

Answer: (B)

As , $B=\frac{{\mu }_0}{4\pi }\frac{2i_D}{r}=\frac{{\mu }_0}{4\pi }\times {\epsilon }_0\frac{d{\varphi }_E}{dt}$
$=\frac{{\mu }_0}{2\pi }\frac{2i_D}{r}=\frac{{\mu }_0}{4\pi }\frac{2}{r}\times {\epsilon }_0\frac{d{\varphi }_E}{dt}$
$=\frac{{\mu }_0{\epsilon }_0\pi r^{2}dE}{2\pi rdt}$
$=\frac{{\mu }_0{\epsilon }_{0}r}{2}\frac{dE}{dt}$