Name: Electric Field of a Sphere
Uploaded: 2019-07-19
Duration: 5 min 10 s
Description: This video demonstrates how an electric field varies as you move away from a point charge or a uniform charge distribution on a sphere. Watch this video.

Question

State Gauss's law in electrostatics and write in its mathematical form.Calculate the electric field $\vec{E}$ at point $P$ due to charges this spherical shell, shown in figure (1) What will be the field $\vec{E}$ shown in fig (2) and (3)? Given the surface charge density is $σ$ .

Accepted Answer

Gauss Law for electrostatics states that the total electric flux passing through a closed surface equals the enclosed charge in the surface divided by the permittivity of the medium. Mathematically it is written as:

$\oint Eds = \frac{q}{ε_{0}}$

Electric field due to a uniformly charged thin shell:
In the diagram, $O$ is the centre of the spherical shell of radius $R$ , and charge enclosed by the spherical shell is $q$ . Let a point $P$ is outside the spherical shell, where we have to calculate the electric field. The distance between the centre of the spherical shell and the point A is $r$ . The total charge on the Gaussian surface of radius $R$ is,

$q = σ (surface area) = σ 4 {πR}^{2}$ .

Hence $\oint Eds = \frac{q (4 π R^{2}) σ}{ε_{0}} or E \oint ds = \frac{q (4 π R^{2}) σ}{ε_{0}}$ .

Case (1) If the point $P$ lies outside the surface of the shell at a distance $r$ from the centre of the sphere

As $\oint E dS = \oint dS = E . 4 {πr}^{2}$ we have $E (4 {πr}^{2}) = \frac{q (4 {πR}^{2}) σ}{ε_{0}} or E = \frac{σ}{ε_{0}} . \frac{R^{2}}{r^{2}} (for r > R)$

Case (2) In figure (2) if the point lies at the surface of the sphere i.e $R = r$ , so we have,

$E = \frac{σ}{ε_{0}}$ (Maximum)

Case (3), In figure (3) The point lies inside the spherical shell. There is no charge inside a spherical shell hence the field is,

$\frac{E = 0}{}$

State Gauss's law in electrostatics and write in its mathematical form.Calculate the electric field $\vec{E}$ at point $P$ due to charges this spherical shell, shown in figure (1) What will be the field $\vec{E}$ shown in fig (2) and (3)? Given the surface charge density is $σ$ .

Important Questions on Electric Charges and Fields

Learn and Prepare for any exam you want !

State Gauss's law in electrostatics and write in its mathematical form.Calculate the electric field E→ at point P due to charges this spherical shell, shown in figure (1) What will be the field E→ shown in fig (2) and (3)? Given the surface charge density is σ.

Important Questions on Electric Charges and Fields

Learn and Prepare for any exam you want !

State Gauss's law in electrostatics and write in its mathematical form.Calculate the electric field $\vec{E}$ at point $P$ due to charges this spherical shell, shown in figure (1) What will be the field $\vec{E}$ shown in fig (2) and (3)? Given the surface charge density is $σ$ .