Question

What will be the electric flux through the sphere $S_1$ if a medium of dielectric constant ${ϵ}_r$ is introduced in the space inside $S_1$ in place of air

• A. $\frac{20}{{ϵ}_0{ϵ}_r}$
• B. $\frac{40}{{ϵ}_0{ϵ}_r}$
• C. $\frac{20{ϵ}_r}{{ϵ}_0}$
• D. $\frac{40{ϵ}_r}{{ϵ}_0}$

Answer 1

The correct option is A $\frac{20}{{ϵ}_0{ϵ}_r}$

We know that flux is given by $\frac{q}{ϵ}$ where q is charge inside the closed area and $ϵ$ is the permittivity of space.

Here, for sphere $S_1$, relative permittivity is ${ϵ}_r$

Hence, permittivity$=ϵ={ϵ}_r{ϵ}_o$

Now, flux through $S_1={\varphi }_1=\frac{20}{{ϵ}_o{ϵ}_r}$

Answer-(A)