# Electric field Inside the Spherical Shell

## Electric field Inside the Spherical Shell

The force felt by a unit positive charge or test charge when its kept near a charge is called Electric Field. It is also defined as the region which attracts or repels a charge. The electric field is a vector quantity and it is denoted by E. the standard units of the electric field is N/C.

To evaluate electric field inside the spherical shell, let’s take a point P inside the spherical shell. By symmetry, we again take a spherical Gaussian surface passing through P, centred at O and with radius r.

Now according to Gauss’s Law:

$$\phi \,\,=\,\,\frac{q}{{{\varepsilon }_{0}}}$$.

The net electric flux will be E x 4πr². But the enclosed charge q will be zero, as we know that surface charge density is dispersed outside the surface, therefore there is no charge inside the spherical shell. Then by Gauss’s Law:

E x 4πr² = 0

E = 0

Therefore, there is no electric field inside the spherical shell because of absence of enclosed charge.