Question

What is Gauss' law? Find the formula for the intensity of electric field produced due to a point charge with the help of it.

Hint:

Gauss' law simplifies calculations for symmetric charge distributions.

Answer 1

Step 1: Gauss' law states that the total electric flux \( \Phi \) through a closed surface is equal to the charge enclosed divided by the permittivity of free space: \[ \oint \vec{E} \cdot d\vec{A} = \frac{q}{\varepsilon_0} \] Step 2: Consider a point charge \( q \) at the center of a spherical surface of radius \( r \): \[ E \cdot 4 \pi r^2 = \frac{q}{\varepsilon_0} \] Step 3: Solving for the electric field: \[ E = \frac{1}{4 \pi \varepsilon_0} \cdot \frac{q}{r^2} \] \[ \boxed{E = \frac{1}{4 \pi \varepsilon_0} \cdot \frac{q}{r^2}} \]