In a certain region, uniform electric field `E=-E_0hatk` and magnetic field `B = B_0hatk` are present. At time `t = 0`, a particle of mass m and charge q is given a velocity `v = v j + v k`. Find the minimum speed of the particle and the time when it happens so.

Answer

5

Explanation

Path of the particle is circle in xz plane in magnetic field centre at `(2,0,0)` and it enter in electic field at `(2,0,2)` parallel to `x`-axis so
From O to A `=T/4=(pim)/(2qB)=(pi)/20s`
A to P `=1/10s`
Total `=((pi+2)/20)sv_(z)=u_(z)+a_(z)t=10m//s`
`( :' a_(z)=100m//s^(2))`
`v=10sqrt(5)`