Question

Eight charges $1\mu \text{C},-7\mu \text{C},-4\mu \text{C},10\mu \text{C}$, $2\mu \text{C},-5\mu \text{C},-3\mu \text{C}$ and $6\mu \text{C}$ are situated at the eight corners of a cube of side $20\text{cm}$. A spherical surface of radius $80\text{cm}$ encloses this cube. The centre of the sphere coincides with the centre of the cube. Then, the total outgoing flux from the spherical surface (in units of $\text{V-m}$) is,

• A. $36\pi \times {10}^3$
• B. $684\pi \times {10}^3$
• C. Zero
• D. $81\pi \times {10}^3$

Answer 1

The correct option is C Zero

The spherical surface encloses the cube hence the total charge enclosed by the sphere is,
$q_{encl}=1\mu \text{C}+(-7\mu \text{C})+(-4\mu \text{C})+10\mu \text{C}+2\mu \text{C}+(-5\mu \text{C})+(-3\mu \text{C})+6\mu \text{C}$

$\Rightarrow q_{encl}=0$

Applying Gauss's law to the spherical surface,

${\varphi }_{\text{total}}=\frac{q_{encl}}{{ϵ}_0}$

$\therefore {\varphi }_{\text{total}}=0$

Hence, $\left(C\right)$ is the correct answer.