Question

What will be the total flux through the faces of the cube with side of the length a if A charge q is placed at

i) A : a corner of the cube

ii) B : mid of an edge of the cube

iii) C : centre of a face of the cube

iv) D : mid point of B and C

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Answer 1

Answer:

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Answer 2

Answer:

We shall be applying Gaussian Law for Electrostatic in each of the cases. We also need to think of placing the charges at centre of the shape .

For example :

• When a charge is being placed at A , which is the vertex , we can consider 8 cubes around the point such that the charge remains at the centre.

Calculation:

When Charge is at A :

8 cubes surrounding the charge at A , so net flux will be equally divided among 8 cubes .

So flux through the given cube will be ⅛ times as that of whole structure ;

$\boxed{ \phi = \dfrac{1}{8} \bigg\{ \dfrac{q}{ \epsilon_{0} } \bigg\}}$

When Charge is at B :

4 cubes can be placed to make the charge located at centre of structure.

So flux through 1 cube will be ;

$\boxed{ \phi = \dfrac{1}{4} \bigg\{ \dfrac{q}{ \epsilon_{0} } \bigg\}}$

When Charge is at C :

2 cubes can be placed to make the charge located at centre , so flux through 1 cube will be ;

$\boxed{ \phi = \dfrac{1}{2} \bigg\{ \dfrac{q}{ \epsilon_{0} } \bigg\}}$

When Charge is at D :

Flux will be equally shared between 2 cubes and hence flux through 1 cube will be :

$\boxed{ \phi = \dfrac{1}{2} \bigg\{ \dfrac{q}{ \epsilon_{0} } \bigg\}}$