JEE MAIN - Physics (2018 - 15th April Morning Slot - No. 5)
A charge $$Q$$ is placed at a distance $$a/2$$ above the center of the square surface of edge a as shown in the figure.
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The electric flux through the square surface is
The electric flux through the square surface is
$${Q \over {{ \in _0}}}$$
$${Q \over {2{ \in _0}}}$$
$${Q \over {3{ \in _0}}}$$
$${Q \over {6{ \in _0}}}$$
Explanation
As in a cube there is 6 faces, you can think this surface is one face among 6 faces. If the side of cube is a length then its center will be $${a \over 2}$$ distance from any surface.
So, we can assume point charge Q is at the center of the cube and total electric flux due to this charge will pass evently through the six faces of the cube.
So, electric flux through one face will be $${1 \over 6}$$. of the total electric flux.
Flux through 6 faces of the cube $$ = {Q \over {{\varepsilon _0}}}$$
$$\therefore\,\,\,\,$$ Flux through 1 face of the cube = $${Q \over {6{\varepsilon _0}}}$$
So, we can assume point charge Q is at the center of the cube and total electric flux due to this charge will pass evently through the six faces of the cube.
So, electric flux through one face will be $${1 \over 6}$$. of the total electric flux.
Flux through 6 faces of the cube $$ = {Q \over {{\varepsilon _0}}}$$
$$\therefore\,\,\,\,$$ Flux through 1 face of the cube = $${Q \over {6{\varepsilon _0}}}$$
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