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

The `y-` coordinate at the highest point of trajectory is

Options

A. `(4m)/(qB_(0)^(2))`
B. `(2m)/(qB_(0)^(2))`
C. `(mE_(0))/(qB_(0)^(2))`
D. `(4mE_(0))/(qB_(0))`

Answer

C

Explanation

`Vy=(E_(0))/(B_(0))sin ((qB_(0))/(m)t),int_(0)^(y)dy=int_(0)^(t)(E_(0))/(B_(0))sin ((qB_(0))/(m)t)dt`
`y=(mE_(0))/(qB_(0)^(2))[1-cos((qB_(0))/(m)t)],y_(max)=(mE_(0))/(qB_(0)^(2))`