In a region where there is a uniform 0195 T magnetic field p

In a region where there is a uniform 0.195 T magnetic field perpendicular to the xy plane, a stream of protons is to be shot from the origin at a fixed initial speed v₀ (see figure below).

(a) At what angle ₀ must the velocity vector v₀ be directed in order for the protons to reach as great a height y as possible?
₀ =  

(b) If the maximum height is 1.18 m, what is the initial speed of the protons?

Please Explain. Thank you.

Solution

a)

The protons will always travel in a circular path for any angle and the radius of the path is constant.

So, the maximum height will be reached when the maximum height is the diameter of the circular path

So, the angle must be 0 degrees <-------answer

b)

For the circualr motion,

centripetal force = Lorentz force

So, mv^2/r = qvB

So, r = mv/qB = 1.67*10^-27*vo*/(1.6*10^-19*0.195)

So, r = 5.35*10^-8*vo m

Now, for maximum height , h = 2r

So, 1.18 = 2*5.35*10^-8*vo

So, vo = 1.1*10^7 m/s <----------answer