What will be the total electric flux through the faces of a cube of side length $a$ if a charge $q$ is placed at:
$(a)$ $A$: a corner of the cube.
$(b)$ $B$: the midpoint of an edge of the cube.
$(a)$ $A$: a corner of the cube.
$(b)$ $B$: the midpoint of an edge of the cube.
(N/A) cube has $8$ corners. If a charge $q$ is placed at one corner,it is shared equally by $8$ identical cubes surrounding that corner.
Therefore,the electric flux through one cube is given by Gauss's Law as:
$\phi = \frac{1}{8} \times \frac{q}{\epsilon_{0}} = \frac{q}{8 \epsilon_{0}}$
$(b)$ If the charge $q$ is placed at $B$,the midpoint of an edge of the cube,it is shared equally by $4$ identical cubes.
Therefore,the electric flux through one cube is:
$\phi = \frac{1}{4} \times \frac{q}{\epsilon_{0}} = \frac{q}{4 \epsilon_{0}}$
Therefore,the electric flux through one cube is given by Gauss's Law as:
$\phi = \frac{1}{8} \times \frac{q}{\epsilon_{0}} = \frac{q}{8 \epsilon_{0}}$
$(b)$ If the charge $q$ is placed at $B$,the midpoint of an edge of the cube,it is shared equally by $4$ identical cubes.
Therefore,the electric flux through one cube is:
$\phi = \frac{1}{4} \times \frac{q}{\epsilon_{0}} = \frac{q}{4 \epsilon_{0}}$
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