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A disc of radius a//4 having a uniformly...

A disc of radius `a//4` having a uniformly distributed charge `6C` is placed in the x-y plane with its centre at `(-a//2, 0, 0)`. A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from `x=a//4` to `x=5a//4`. Two point charges `-7C` and `3C` are placed at `(a//4, -a//4, 0)` and `(-3a//4, 3a//4, 0)`, respectively. Conisder a cubical surface formed by isx surfaces `x=+-a//2`, `y=+-a//2`, `z=+-a//2`. The electric flux through this cubical surface is

A

` ( -2 C)/(varepsilon_0)`

B

` (2C)/( varepsilon_0)`

C

`( 10C)/(varepsilon_0)`

D

`(12 C)/(varepsilon_0)`

Text Solution

Verified by Experts

The correct Answer is:
A
Electric flux through the cubical surcace `= q/(varepsilon_0)` where `q` is the net chaege eneclosed in the surface. Since half the disc lies inside the surgace one fourth of the rod lies inside the surface, point charge `- 7 C` lies inside the sureace and point charge `3C` lies outside the surface, the charge enerclosed in the suraface is
` q = (6 C)2 + (8C)/4 - 7 C`
`= 3 C + 2 C - 7 C =- 2 C`
`:.` Electric flux `= (-2 C)/(varepsilon_0)`.
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