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Q.

A parallel plate capacitor made of circular plates each of radius $R = 6 cm$ has a capacitance $C = 100 pF .$ The capacitor is connected to a 230 V AC supply with a angular frequency of 300 rad/sec. Find the amplitude of B at a point 3 cm from the axis between the plates.

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a

$1 .63 \times 10^{- 11} T$

b

$4 .63 \times 10^{- 11} T$

c

$2 .63 \times 10^{- 11} T$

d

$3 .63 \times 10^{- 11} T$

answer is A.

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Detailed Solution

$X_{c} = \frac{1}{ωC} = \frac{1}{300 \times 100 \times 10^{- 12}} = \frac{10^{8}}{3} Ω i_{rms} = \frac{V_{rms}}{X_{c}} = \frac{230}{\frac{10^{8}}{3}} = 6 .9 \times 10^{- 6} A For r < R, B_{rms} = \frac{μ_{0}}{2 π} \frac{i_{rms}}{R^{2}} r = \frac{2 \times 10^{- 7} \times 6.9 \times 10^{- 6} \times (0.03)}{{(0.06)}^{2}} = 1 .15 \times 10^{- 11} T B_{0} = \sqrt{2} B_{rms} = \sqrt{2} \times 1 .15 \times 10^{- 11} = 1 .63 \times 10^{- 11} T$

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A parallel plate capacitor made of circular plates each of radius R=6 cm has a capacitance C=100 pF. The capacitor is connected to a 230 V AC supply with a angular frequency of 300 rad/sec. Find the amplitude of B at a point 3 cm from the axis between the plates.