Question

A conducting sphere has a radius 30 cm. If the dielectric strength of surrounding air is 3 x 10 V/m, the maximum amount of charge the sphere can hold in micro-coulombs is

Answer 1

Answer:

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Answer 2

The correct question: A conducting sphere has a radius 30 cm. If the dielectric strength of surrounding air is 3 x $10^{6}$ V/m, the maximum amount of charge the sphere can hold in micro-coulombs is

1) 0.03

2) 0.3

3) 3

4) 30.

The correct answer is option (4) 30 μC.

Given:

The radius of the sphere, r = 30 cm = 0.3 m.

The dielectric strength of surrounding air = 3 x $10^{6}$ V/m.

To Find:

Using the given values, we have to find  the maximum amount of charge the sphere can hold in micro-coulomb.

Solution:

The dielectric strength is given by the equation,

E = $\frac{KQ}{r^{2} }$

E = $\frac{1}{4\.pi.ε_{o} }. \frac{Q}{r^{2} }$

$3$ × $10^{6}$ $= (9$ × $10^{9})$.$\frac{Q}{(0.3)^2}$

$Q =$ $\frac{(3.10^{6}.(0.3)^2 )}{9.10^{9} }$

$Q = 3$ × $10^{-5}$

$i.e., Q = 30$ μC.

Hence, the maximum amount of charge the sphere can hold in micro-coulomb is 30 μC.

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