1.

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 magneticfield 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

Answer»

`(4M)/(qB_(0)^(2))`
`(2m)/(qB_(0)^(2))`
`(mE_(0))/(qB_(0)^(2))`
`(4mE_(0))/(qB_(0))`

SOLUTION :`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))`


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