Question

State coulombs law & express in vector form, derive it using Gauss theorem.

Answer 1

states that the electrostatic force between two stationary point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Vector for of Couloms law: F1 = k q1q2 ř21 / [r21]2

From Gauss Theorem:

Draw a Gaussian sphere of radius r at the centre of which charge +q is located

All the points on this surface are equivalent. Due to symmetry, the electric field E has the same magnitude at every point on the surface of the sphere and it is radially outward in direction. Therefore, for a area element dS around any point P on the Gaussian surface both E and dS are directed radially outward, Hence, the angle between E and dS is zero.

The flux passing through the area 

Answer 2

Answer:

Explanation:

According to the Gauss law, the total flux linked with a closed surface is 1/ε0 times the charge enclosed by the closed surface.

∮E⃗ .d⃗ s=1∈0q .

According to Gauss Law,

Φ = → E.d → A

Φ = Φcurved + Φtop + Φbottom

Φ = → E . d → A = ∫E . dA cos 0 + ∫E . dA cos 90° + ∫E . dA cos 90°

Φ = ∫E . dA × 1

Due to radial symmetry, the curved surface is equidistant from the line of charge and the electric field in the surface has a constant magnitude throughout.

Φ = ∫E . dA = E ∫dA = E . 2πrl

The net charge enclosed by the surface is:

qnet = λ.l

Using Gauss theorem,

Φ = E × 2πrl = qnet/ε0 = λl/ε0

E × 2πrl = λl/ε0

E = λ/2πrε0