Question

A charge Q is uniformly distributed on the surface of a cube and there is no other charge in consideration. Divergence of electric field is​

Answer 1

Answer:

HOPE IT HELPS.!!!!!!.

Explanation:

Since, charge q is placed inside cube, flux through cube is

ϕ=

ϵ

o

q

Now, a cube has 6 faces with equal area.

Hence, flux through each face will be same and total flux through all faces is

ϵ

o

q

Hence, flux through each face is

6ϵ

o

q

.

Answer 2

Given:

A charge Q is uniformly distributed on the surface of a cube and there is no other charge in consideration.

To find:

Divergence of electric field.

Calculation:

General expression for Divergence is as follows:

$\boxed{ \bf{ \nabla \: . \: E = \dfrac{ \rho}{ \epsilon_{0} } }}$

Here , E is electric field , $\rho$ is charge density.

Now , considering the cube to be non-conducting , we can say that flux from the cube is equally divided among the 6 surfaces.

$\rm{ \therefore \: \phi = \dfrac{q}{6 \epsilon_{0}}}$

Similarly , divergence will also be equally divided among the 6 faces of the cube;

$\therefore \: \rm{ \nabla \: . \: E = \dfrac{ \rho}{ 6\epsilon_{0} } }$

So, final answer is:

$\boxed{ \: \bf{ \nabla \: . \: E = \dfrac{ \rho}{ 6\epsilon_{0} } }}$