Question

A charge of $1\text{C}$ is located at the centre of a sphere of radius $10\text{cm}$ whose centre coincides with that of a cube of side $20\text{cm}$. The ratio of the outgoing flux from the sphere to the outgoing flux from the cube will be

• A. more than one
• B. less than one
• C. one
• D. nothing can be said

Answer 1

The correct option is C one

The charge $q=1\text{C}$ is placed at the centre of a sphere of radius $R=10\text{cm}$. As the side of the square is $20\text{cm}$, so the cube will contain the sphere as shown.


As we can see in this figure, the field lines originating from the charge will first intersect the sphere followed by the cube. This tells us that the same number of field lines will intersect the sphere and the cube.

$\therefore {\varphi }_{\text{cube}}={\varphi }_{\text{sphere}}$

or, $\frac{{\varphi }_{\text{sphere}}}{{\varphi }_{\text{cube}}}=1$

So, option $\left(c\right)$ is correct.