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 $=\frac{Q}{{\epsilon }_{0}4\pi }$
Flux associated with base of cone is $\varphi =\frac{Q2\pi }{4\pi {\epsilon }_0}(1-cos{60}^0)=\frac{Q}{4{\epsilon }_0}$
Flux with curved surface $={\varphi }_{net}-\varphi =\frac{Q}{{\epsilon }_0}-\frac{Q}{4{\epsilon }_0}$
$=\frac{3}{4}\frac{Q}{{\epsilon }_0}$