Question

A charge ${}^{\prime }{q}^{\prime }$ is placed at one corner of a cube as shown in figure. The flux of electrostatic field $\overrightarrow{E}$ though the shaded area is:

• A. $\frac{q}{48{ϵ}_o}$
• B. $\frac{q}{8{ϵ}_o}$
• C. $\frac{q}{24{ϵ}_o}$
• D. $\frac{q}{4{ϵ}_o}$

Answer 1

The correct option is C $\frac{q}{24{ϵ}_o}$

Total flux through the cube $=\frac{q}{{ϵ}_o}\times \frac{1}{8}=\frac{q}{8{ϵ}_o}$

Total flux through one “outer” face of the cube $=\frac{q}{8{ϵ}_o}\times \frac{1}{3}=\frac{q}{24{ϵ}_o}$
[Because there is flux only through $3$ faces]

Hence, total flux through shaded area,
${\varphi }_T=(\frac{q}{24{ϵ}_o}+\frac{q}{24{ϵ}_o})\times \frac{1}{2}$
[half of each face is shaded]

${\varphi }_T=\frac{q}{24{ϵ}_o}$