A conic surface is placed in a uniform electric field E as shown in figure. 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 `(thetalt45^@)`.

Options

A. `ER[h cos theta + pi(R//2)sin theta]`
B. `ER[h cos theta + piR//2sin theta]`
C. `ER[h cos theta + piRsin theta]`
D. none of these

Answer

A

Explanation

a. Flux entering the cone from side `AB` will ultimately also pass
through areas `A_1` and `A_2`. So,
`phi = EA_1 cos theta + EA_2 cos (90 - theta)`
` = E (1/2 2Rh cos theta + pi/2 R^2 sin theta)`
`= ER [h cos theta + pi (R//2)sin theta]`