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A point charge $q$ is placed at the corner of a cube of side $a$ as shown in the figure. What is the electric flux through the face $A B C D$ ?
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Verified Answer
The correct answer is:
$\frac{q}{24 \varepsilon_{0}}$
If charge is placed at the one corner of a cube, then it can be shared further by 8 cubes.
$\therefore$ Charge on one cube $=\frac{q}{8}$
Now, in any given cube this charge will be touching 3 out of 9 of cube faces. So, the area vector of that side and the electric field vector will be perpendicular. So, flux through those 3 sides will be zero. However, equal amount of flux will flow from other 3 sides.
So, flux through one side $=\left(\frac{q / 8}{3}\right) \cdot \frac{1}{\varepsilon_{0}}=\frac{q}{24 \varepsilon_{0}}$ Hence, flux through one face $(A B C D)=\frac{q}{24 \varepsilon_{0}}$
$\therefore$ Charge on one cube $=\frac{q}{8}$
Now, in any given cube this charge will be touching 3 out of 9 of cube faces. So, the area vector of that side and the electric field vector will be perpendicular. So, flux through those 3 sides will be zero. However, equal amount of flux will flow from other 3 sides.
So, flux through one side $=\left(\frac{q / 8}{3}\right) \cdot \frac{1}{\varepsilon_{0}}=\frac{q}{24 \varepsilon_{0}}$ Hence, flux through one face $(A B C D)=\frac{q}{24 \varepsilon_{0}}$
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