Question

An ellipsoidal gaussion surface with semi major axis a and semi-minor axis b is shown in figure. An electric field $\vec{E} = \frac{C(x\hat{i}+y\hat{j}+z\hat{k})}{(x^2 + y^2 + z^2)^{3/2}}$ exist in space.

• A. Net flux through the gaussion surface is $4\pi C$
• B. Net charge enclosed by gaussion surface is $4\pi C\epsilon_0$
• C. If given surface is a conductor electric potential at all its inside points may be constant for given field function
• D. If given surface is a conductor electric field at all its inside points may be constant for given field function

Answer 1

Answer: (A), (B), (C), (D)

A, B, C, D

Answer 2

The electric field is $\vec{E} = C\frac{\vec{r}}{r^3}$, which is the field of a point charge $q = 4\pi\epsilon_0 C$ at the origin.

(A) By Gauss's law, $\Phi_E = \frac{Q_{enclosed}}{\epsilon_0} = \frac{4\pi\epsilon_0 C}{\epsilon_0} = 4\pi C$.

(B) The net charge enclosed is $q = 4\pi\epsilon_0 C$.

(C) For a conductor in electrostatic equilibrium, $\vec{E}_{inside} = 0$. If $\vec{E}=0$, then the potential is constant.

(D) $\vec{E}_{inside} = 0$, which is a constant value.