Ncert Exercises & Solutions

What will be the total flux through the faces of the cube as given in the figure with a side of length 'a' if a charge q is placed at?

(a) A: a corner of the cube

(b) B: mid-point of an edge of the cube

(d) D: mid-point of B and C

Hint: Use Gauss' law.

Step 1: Find the electric flux in each case passing through the cube.

(a) There are eight corners in a cube so, the total charge for the cube is

\frac{q}{8}

. Thus, the electric flux at

A = \frac{q}{8 ε_{0}}

(b) When the charge q is placed at B, the middle point of an edge of the cube, it is being shared equally by 4 cubes. Therefore, total flux through the faces of the given cube

= q / 4 ε_{0}

(c) When the charge q is placed at C, the centre of a face of the cube, it is being shared equally by 2 cubes. Therefore, total flux through the faces of the given cube

= q / 2 ε_{0}

(d) Similarly, when charge q is placed at D, the mid-point of B and C, it is being shared equally by 2 cubes. Therefore, total flux through the faces of the given cube

= q / 2 ε_{0}

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