Question

Prove that 1/r2 dependence of electric field of a point charge is consistent with the concepts of the electric filed lines.

Answer 1

Given:

A point charge and the electric filed lines.

To Prove:

1/r2 dependence of electric field of a point charge is consistent with the concepts of the electric filed lines.

Solution:

Gauss Law states that,

• Net flux  = Charge enclosed/∈
• Ф = q enclosed/∈

Flux =  electric field x Area.

• Ф = E x A .

Assume a point charge,

• We can imagine a sphere of radius r enclosing the charge.
• Area of such a sphere = 4πr²

Then, applying Gauss Law,

• E x 4πr² = q /∈
• E = q/ 4π∈r²

Therefore Electric field  α 1/r² .

Thus proved the   1/r2 dependence of electric field of a point charge is consistent with the concepts of the electric filed lines.

Answer 2

The answer of this question is in the image given