Question

A right circular imaginary cone is shown in Fig. A, B, and C are the points the plane containing the base of the cone, while D is the point at the vertex of the cone. If ${\varphi }_A,{\varphi }_B,{\varphi }_C$, and ${\varphi }_D$ respectively the flux through the curved surface of the cone when a point charge Q is at points A, B, C, and D, respectively, then

• A. ${\varphi }_A={\varphi }_C\ne 0$
• B. ${\varphi }_D\ne 0$
• C. ${\varphi }_B=\frac{Q}{2{\epsilon }_0}$
• D. ${\varphi }_A={\varphi }_C={\varphi }_D=0$

Answer 1

Answer: (C), (D)

The correct options are
C ${\varphi }_A={\varphi }_C={\varphi }_D=0$
D ${\varphi }_B=\frac{Q}{2{\epsilon }_0}$

When the charge Q is at A,C and D , no charge enclosed within the curve surface. By applying Gauss's law $(\varphi =\frac{Q_{en}}{{ϵ}_0})$, ${\varphi }_A={\varphi }_C={\varphi }_D=0$.
When charge is placed at B, half part of charge $\left(Q/2\right)$ is inside the curved surface.
So, $Q_{en}=Q/2$
thus, ${\varphi }_B=\frac{Q_{en}}{{ϵ}_0}=\frac{Q}{2{ϵ}_0}$