Question

Figure shows an imaginary cube of side $a$. A uniformly charged rod of length $a$ moves towards right at a constant speed $v$. At $t=0$, the right end of the rod just touches the left face of the cube. Which of the following represents the correct graph between electric flux passing through the cube with time?

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

We know from Gauss's Law

$\varphi =\frac{q}{{ϵ}_o}$

where $q$ is the charge enclosed by the gaussian surface.

$\Rightarrow \varphi \propto q$

Now in this given case, at $t=0$ the right end of the rod just touches the left face of the cube. So at $t=0$, the charge inside the cube is zero and hence the flux is zero.

Now the rod starts moving inside the cube. So with time the charge enclosed by the cube increases and hence the flux increses linearly as well until it reaches a maximum when the entire rod is inside the cube.

Then, as the rod starts to move out of the cube the charge enclosed by the cube will decrease linearly with time and hence the flux will also decrease till the entire rod is out of the cube and the flux becomes zero.

Therefore, the electric flux first increases, reaches a maximum value and finally decreases to zero.

This behaviour is shown only in option $\left(b\right)$.