Question 705057

Added on: Sep 19, 2026

SCQHARD

In a non-magnetic material with no free charges and no free currents, the permittivity $\epsilon$ is a function of position. If $\vec{E}$ represents the electric field and $\mu_0, \epsilon_0$ are free space permeability and permittivity respectively, which one of the following expressions is correct?

(A)

$\nabla^2 \vec{E} - \mu_0 \frac{\partial^2(\epsilon\vec{E})}{\partial t^2} - \frac{1}{\epsilon_0} \nabla(\vec{E} \cdot \nabla\epsilon) = 0$

(B)

$\nabla^2 \vec{E} - \mu_0 \frac{\partial^2(\epsilon\vec{E})}{\partial t^2} + \frac{1}{\epsilon_0} \nabla(\vec{E} \cdot \nabla\epsilon) = 0$

(C)

$\nabla^2 \vec{E} - \mu_0 \frac{\partial^2(\epsilon\vec{E})}{\partial t^2} + \nabla(\frac{1}{\epsilon} \vec{E} \cdot \nabla\epsilon) = 0$

(D)

$\nabla^2 \vec{E} - \mu_0 \frac{\partial^2(\epsilon\vec{E})}{\partial t^2} - \nabla(\frac{1}{\epsilon} \vec{E} \cdot \nabla\epsilon) = 0$

Question 705057

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