# A 0.510-m diameter spherical shell is placed in a uniform electric field of magnitude 3.66x10 4 ...

## Question:

A 0.510-m diameter spherical shell is placed in a uniform electric field of magnitude 3.66x10{eq}^4 {/eq} N/C. Find the total electric flux, in NA?1m{eq}^2 {/eq}/C, through the shell.

## Gauss's Law:

For any closed surface, the total electric flux through it is proportional to the net charge enclosed by the closed surface, and is independent of any charge outside the closed surface, which is based on Gauss's Law.

Given Data

• Diameter of a spherical shell, d = 0.510 m
• Uniform electric field in the region, {eq}E\ = 3.66\times 10^4\ N/C{/eq}

Finding the total electric flux ({eq}\phi{/eq}) through the spherical shell

The given spherical shell is a closed surface, for which Gauss's law can be applied as:

• Since the electric field present in the region is uniform, it indicates that the spherical shell doesn't enclose any net charge.
• According to Gauss's law, the net flux through a closed surface depends only on the enclosed charge.
• Now, since, there is no enclosed charge inside the spherical shell, the net flux through the spherical shell (closed surface) will be zero

The total electric flux through the given spherical shell is {eq}0\ N.m^2/C{/eq}