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

A closed spherical surface encloses a charge q at its centre. Show the electric flux through the closed surface is $q / ε_{\circ}$ .

Accepted Answer

Let the radius of closed spherical surface is R.

the electric field at the centre is $\vec{E_{c}}$ $=$ $\frac{1}{4 {πε}_{\circ}}$ $\frac{q}{R^{2}}$ $\hat{r}$

where $\overset{\land}{r}$ = Radial vector from the charge at the centre.

Now d $ϕ = \vec{E}$ . $\hat{r}$ dA

= $\frac{1}{4 πε \circ}$ $\frac{q}{R^{2}}$ . $\hat{r}$ . $\hat{r}$ dA

$=$ $\frac{1}{4 {πε}_{\circ}}$ $\frac{q}{R^{2}}$ dA

we can find net flux by integrating above flux over the surface of the sphere :

$=$ $\oint \frac{1}{4 {πε}_{\circ}} \frac{q}{R^{2}} d A$

$= \frac{1}{4 {πε}_{\circ}} \frac{q}{R^{2}} \oint d A$

$= \frac{1}{4 {πε}_{\circ}} \frac{q}{R^{2}}$ $(4 {πR}^{2})$

$ϕ = \frac{q}{ε_{\circ}}$ Hence proved

A closed spherical surface encloses a charge q at its centre. Show the electric flux through the closed surface is $q / ε_{\circ}$ .

Important Questions on Electric Charges and Fields

Learn and Prepare for any exam you want !

A closed spherical surface encloses a charge q at its centre. Show the electric flux through the closed surface is q/ε∘ .

Important Questions on Electric Charges and Fields

Learn and Prepare for any exam you want !

A closed spherical surface encloses a charge q at its centre. Show the electric flux through the closed surface is $q / ε_{\circ}$ .