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Physics - Electrostatics Question with Solution | TestHub

PhysicsElectrostaticsGauss LawMedium

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In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field. It states that,

"The net electric flux through any closed surface is equal to 1/∊0 times the net electric charge enclosed within that closed surface".

In a region it was found that electric field varies radially as $E = α r^{3}, α$ is constant. Then in the region charge density linked with the field will be :

Options:

Answer:

Solution:

For a radial field $E = α r^{3}$ : $\nabla \cdot E = \frac{1}{r ^{2}} \frac{d}{d r} (r^{2} \cdot α r^{3}) = 5 α r^{2}$

Gauss's law: $ρ = 5 α r^{2} ε_{0}$ .

Subject:PhysicsTopic:ElectrostaticsSubtopic:Gauss Law

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