Question

Charge $Q$ is placed inside cone as shown in figure such that $\theta ={60}^{\circ }$. Flux of electric field associated with curved surface of cone is.

• A. $\frac{Q}{4{\epsilon }_0}$
• B. $\frac{Q}{2{\epsilon }_0}$
• C. $\frac{3Q}{4{\epsilon }_0}$
• D. $\frac{Q}{3{\epsilon }_0}$

Answer 1

The correct option is C $\frac{3Q}{4{\epsilon }_0}$

Flux per unit solid angle of charge is $=\frac{Q}{{ϵ}_{o}4\pi }$
Solid angle in terms of plane angle is given by,
$\Omega =2\pi (1-cos\theta )$
Flux associated with base of cone is $\varphi =\frac{Q}{4\pi {ϵ}_o}\Omega =\frac{Q}{4\pi {ϵ}_o}2\pi (1-cos{60}^{\circ })=\frac{Q}{4{ϵ}_o}$
Flux associated with the curved surface $={\varphi }_{net}-\varphi =\frac{Q}{{ϵ}_o}-\frac{Q}{4{ϵ}_o}$
$=\frac{3}{4}\frac{Q}{{ϵ}_o}$