A particle with mass m and positive charge q released from rest at the origin as shown in figure. There is a uniform electric field `E_(0) `in `+y` direction and uniform magnetic field `B_(0)` directed out of the page. The path of the particle as shown is called cycloid. The particle always moves in `x-y` plane. The velocity at any time t after the start is given as

Speed of the particle at a general point `P(x,y)` is given by

Options

A. `sqrt((2qE_(0)sqrt(x^(2)+y^(2)))/(m))`
B. `sqrt((2qE_(0)y)/(m))`
C. `sqrt((2qE_(0)x)/(m))`
D. `(E_(0))/(B_(0))`

Answer

B

Explanation

`(1)/(2)mv^(2)=qE_(0)y" "v=sqrt((2qE_(0)y)/(m))`