Question

A conic surface is placed in a uniform electric field $E$ as shown such that field is perpendicular to the surface on the side $A B$. The base of the cone is of radius $R$ and height of the cone is $h$.

The angle of cone is $\theta$ as shown. Find the magnitude of that flux which enters the cone curved surface from left side. Don't count the outgoing flux. $\left(\theta<45^{\circ}\right)$

• A. $E R[h \cos \theta+\pi(R / 2) \sin \theta]$
• B. $E R[h \sin \theta+\pi(R / 2) \cos \theta]$
• C. $E R[h \cos \theta+\pi R \sin \theta]$
• D. None of these

Answer 1

Answer: (A)

Flux entering the cone from side $A B$ will ultimately also pass through area $A_{1}$ and $A_{2}$.

So, $\phi=E A_{1} \cos \theta+E A_{2} \cos \left(90^{\circ}-\theta\right)$
$=E\left(\frac{1}{2} 2 R h \cos \theta+\frac{\pi}{2} R^{2} \sin \theta\right)$
$=E R(h \cos \theta+\pi(R / 2) \sin \theta)$