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Question: The diameter of each plate of an air capacitor is 4 cm. To make the capacity of this plate capacitor...

The diameter of each plate of an air capacitor is 4 cm. To make the capacity of this plate capacitor equal to that of diameter sphere, the distance between the plates will be

A

B

C

1 cm

D

1×10−3 cm1 \times 10 ^ { - 3 } \mathrm {~cm}

Answer

Explanation

Solution

Capacity of spherical conductor of 20 cm diameter

C1=4πε0r=4πε0×10C _ { 1 } = 4 \pi \varepsilon _ { 0 } r = 4 \pi \varepsilon _ { 0 } \times 10

Capacity of parallel plate air capacitor

C2=ε0Ad=ε0[π(2)2]d=ε0×4πdC _ { 2 } = \frac { \varepsilon _ { 0 } A } { d } = \frac { \varepsilon _ { 0 } \left[ \pi ( 2 ) ^ { 2 } \right] } { d } = \frac { \varepsilon _ { 0 } \times 4 \pi } { d }

Hence C1=C2C _ { 1 } = C _ { 2 } ⇒ 40πε0=4πε0d40 \pi \varepsilon _ { 0 } = \frac { 4 \pi \varepsilon _ { 0 } } { d }⇒ d=10−3 md = 10 ^ { - 3 } \mathrm {~m}