Find momentum of particle in B field

[zezima1]

Homework Statement

The problem statement is on the attached file.

Homework Equations

Lorentz force law maybe.

The Attempt at a Solution

My teacher actually did this, by calculating the radius of the circle that the particle would orbit to find the momentum using the cyclotron equation.
But I would like to ask if there are other methods than just this one. My curiosity comes the fact that since I could remember how my teacher did it, I became curious on whether other approaches to the problem could be taken.
Could you for instance integrate over the force to get the total change in momentum? I tried this but came in trouble, because v is unknown.
So yes, is it possible to do this problem in other ways than using the cyclotron equation?

 

[Sleepy_time]

Hi zezima1. So in the question the B field and velocity are perpendicular, so the force on the charge is always perpendicular to it's velocity, this means the speed will never change, it only changes direction. You can then use that the magnetic force is equivalent to the centripetal force to get an equation for mv (i.e. the momentum) in terms of the radius of the circle the charge goes around. You can get the radius by using the equation for a circle centred at (0,0):

x²+y²=r²​

This equation must go through the points (0,-r) and (a,d-r) (I'm just the x-axis as going from left to right and the y-axis upwards). I hope this helps.