A sheet of semi circular paper (radius R) is turned around the centre in to a cone as shown. If a point charge +q is kept at the vertex of thecone, the electric flux that comes out of the base of the cone is

Options

A. `q/(4 epsilon_(0))`
B. `(q(2-sqrt(3)))/(4epsilon_(0))`
C. zero
D. `q/(2 epsilon_(0))`

Answer

B

Explanation

The circumference of the base of the cone is semi circumference of the paper which is pr. Hence the radius of the base is R/2. The sime vertical angle of the cone is `30^(@)`, sicne `sin q=(R//2)//R=1//2`. The solid angle subtended by the base at the vertex is `2p(1-cos q)=pi(2-sqrt(3))`. The flux is uniformly distributed so for 4p steradians it is `q//e_(a)`, for steradians it is `(q(2-sqrt(3)))/(4epsilon_(0))`