Question

A conic surface is placed in a uniform electric field E as shown in Fig. such that the field is perpendicular to the surface on the side AB. The base of the cone is of radius R, and the height of the cone is h. The angle of the cone is $\theta$. Find the magnitude of the flux that enters the cone's curved surface from the left side. Do not count the outgoing flux $(\theta <{45}^{\circ })$ :

• A. $ER[h\cos \theta +\pi (R/2\left)\sin \theta \right]$
• B. $ER[h\sin \theta +\pi R/2\cos \theta ]$
• C. $ER[h\cos \theta +\pi R\sin \theta ]$
• D. none of these

Answer 1

The correct option is A $ER[h\cos \theta +\pi (R/2\left)\sin \theta \right]$

Flux entering the cone from side AB will ultimately also pass through areas $A_1$ and $A_2$. So,
$\varphi =E{A}_{1}cos\theta +E{A}_{2}cos(90-\theta )$
$=E(\frac{1}{2}2Rhcos\theta +\frac{\pi }{2}{R}^{2}sin\theta )$
$=ER[hcos\theta +\pi (R/2\left)sin\theta \right]$