State and Explain Gauss's law in electrostatic.

Gauss’s Theorem Statement:

According to Gauss’s theorem the net-outward normal electric flux through any closed surface of any shape is equivalent to 1/ε0 times the total amount of charge contained within that surface.

Proof of Gauss’s Theorem Statement:

Let the charge be = q
Let us construct the Gaussian sphere of radius = r

Now, Consider, A surface or area ds having ds (vector)

Normal having the flux at ds:

Flux at ds:

d e = E (vector) d s (vector) cos θ

But , θ = 0

Therefore, Total flux:

C = f d Φ

E 4 π r2

Therefore,

σ = 1 / 4πɛo q / r2 × 4π r2

σ = q / ɛo

Gauss law

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

\oint \vec{E} . \vec{d} s = \frac{1}{\in_{0}} q

Why Equipotential surfaces are always at right angles to lines of electric force?

For an equipotential surface,

Change in potential difference, V = 0

Work done = qV = q0 = 0

Also,

Work done = Fs cosA = 0

Where, F = Force due to charges,

s = distance between charged bodies, and

A = angled between direction of F and s

Since, the equipotential surface is formed due to cancellation of equal and opposite electric fields, F and s cannot be 0.

So, Work done = 0 if and only if cos A = 0 A = 90

Hence, the equipotential surfaces are always at right angles to lines of electric force.

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20 Physics -- Electric Field

State and Explain Gauss's law in electrostatic.

1 Answers

State and prove Gauss Theorem in electrostatics

Gauss’s Theorem Statement:

Proof of Gauss’s Theorem Statement:

Gauss law

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