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., $d E / d t$ between the plates

• A. $\frac{\mu_{0} i}{2 \pi r}$
• B. $\frac{\varepsilon_{0} \mu_{0} r}{2} d E / d t$
• C. zero
• D. $\frac{\mu_{0} i}{2 \pi}$

Answer 1

Answer: (B)

As , $B =\frac{\mu_{0}}{4 \pi} \frac{2 i_{D}}{r}=\frac{\mu_{0}}{4 \pi} \times \varepsilon_{0} \frac{d \phi_E}{d t}$
$=\frac{\mu_{0}}{2 \pi} \frac{2 i_{D}}{r}=\frac{\mu_{0}}{4 \pi} \frac{2}{r} \times \varepsilon_{0} \frac{d \phi_E}{d t}$
$=\frac{\mu_{0} \varepsilon_{0} \pi r^{2} d E}{2 \pi r d t}$
$=\frac{\mu_{0} \varepsilon_{0} r}{2} \frac{d E}{d t}$