Name: Continuous Charge Distribution
Uploaded: 2019-07-19
Duration: 5 min 39 s
Description: This video will help us understand the necessity of continuous charge distribution and learn about the concept of linear charge density. Learn more.

Question

Find electric field inside a uniformly charged thin spherical shell having charge

Q

. If a charge

q

is placed at the centre of this shell, how the electric field will change?

Accepted Answer

Gauss’s law- Gauss’s law is defined as the total electric flux through any closed surface is equal to the total charge enclosed by the surface.
Surface on which Gauss’s law is Applicative is known as Gaussian surface which need not be a real surface.
Let, a thin spherical shell of radius $R$ having a positive charge $q$ is uniformly distributed on the surface. As the electric field is symmetrical and directed radially outward, it means that the charge is distributed uniformly.

Electric field outside the shell:

For point $r > R$ ; let a spherical Gaussian surface of radius $r$ .

Using gauss law, $\oint E . d s = \frac{q_{e n c}}{ε_{\circ}}$

Since $\vec{E}$ is perpendicular to Gaussian surface, angle between $\vec{E}$ is $0$

Also, $\vec{E}$ being constant, can be taken out of integral.

So, $E (4 π r^{2}) = \frac{q}{ε_{\circ}}$

So, $E = \frac{1}{4 π ε_{\circ}} \frac{q}{r^{2}}$

Thus, the electric field outside a Shell is the same.

Inside the shell:
Let, a Gaussian surface concentric with the shell of radius $r (r > R)$

So, $\oint E . d s = E (4 π r^{2})$

According to gauss law,

$E (4 π r^{2}) = \frac{Q_{e n c}}{ε_{\circ}}$

The charge enclosed inside the spherical shell is $0$ .

So, $E = 0$

Therefore, due to the electric field, the uniformly charged spherical shell is zero at all points inside the shell.

Find electric field inside a uniformly charged thin spherical shell having charge $Q$ . If a charge $q$ is placed at the centre of this shell, how the electric field will change?

Important Questions on Electric Charges and Fields

Learn and Prepare for any exam you want !

Find electric field inside a uniformly charged thin spherical shell having charge Q. If a charge q is placed at the centre of this shell, how the electric field will change?

Important Questions on Electric Charges and Fields

Learn and Prepare for any exam you want !

Find electric field inside a uniformly charged thin spherical shell having charge $Q$ . If a charge $q$ is placed at the centre of this shell, how the electric field will change?