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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".

Consider a cube of side "a" placed such that it faces are parallel to $x - y$ ; $y - z$ \& $z - x$ plane. (see figure) An electric field exists in the region as $y \hat{i} + x \hat{j} = E$ . The net charge enclosed in the cube will be :-

Options:

Answer:

Solution:

$E = y \hat{i} + x \hat{j} \Rightarrow \nabla \cdot E = \frac{\partial y}{\partial x} + \frac{\partial x}{\partial y} = 0$

By Gauss's law $ρ = ε_{0} (\nabla \cdot E) = 0$ , so the cube encloses zero net charge.

Subject:PhysicsTopic:ElectrostaticsSubtopic:Gauss Law

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