First slide

Maxwell's Equations

Question

An AC rms voltage of 2 V having a frequency of 50 kHz is applied to a condenser of capacity of 10 μF. The maximum value of the magnetic field between the plates of the condenser, if the radius of plate is 10 cm is

Difficult

A

0.4 $π$ μT
B

4 $π$ μT
C

$4 \sqrt{2}$ $π$ μT
D

40 $π$ μT

Solution

$\begin{array}{rcl} i_{0} & = & \frac{V_{0}}{X_{C}} \\ = & \frac{\sqrt{2} V_{rms}}{X_{C}} \\ = & \frac{\sqrt{2} V_{rms}}{\frac{1}{ωc}} \\ = & \sqrt{2} V_{rms} ω c \\ = & \sqrt{2} x 2 x 2 π x 50 x 10^{3} x 10 x 10^{- 6} \\ = & 2 π \sqrt{2} Amp \\ \oint \bar{B} . \bar{d l} & = & μ_{0} i_{0} \\ B . 2 πR & = & μ_{0} i_{0}; \\ B . 2 π 10^{- 1} & = & 4 π x 10^{- 7} \times 2 π \sqrt{2} \\ B & = & 4 \sqrt{2} π μT \end{array}$

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