Finding magnetic field magnitude from electron cyclotron radius and speed

[bidhati]

Homework Statement

A stream of 100 eV electrons, each with speed v = 5.9 × 106 ms−1, traveling horizontally along the x-axis in the positive x-direction enters a region pervaded by a uniform magnetic field B. The electrons then describe a circle with radius R in the horizontal xy-plane, circulating anticlockwise as viewed from above.
Starting from the equation Fm = q(v × B), derive an expression for the
radius, R, of the circular path followed by the electrons. If R = 2.0 cm, find the magnitude, B, of the uniform magnetic field.

Homework Equations

1. Fm = q(v x B)

2. Rc = mv / qB

3. T = 2 pi mv /vqB = 2 pi Rc / v =2 pim / qB

4. Fm = q v b sin Theta

The Attempt at a Solution

ok the only known variables I have are
v = 5.9 × 106 ms−1
Rc = 2.0

and I know from the next question on my paper that fromthe expression derived I have to evaluate T so therefore T v and Rc must be in the final equation.

The problem I am getting is trying to eliminate q
I started by eliminating Fm by setting equations 1 and 4 =
but the q on the left is magnitude q and the q on the right is not. so I am getting confused now, have rearranged all the equations and substiuting each different variable but the more I carry on I just end up with a HUGE equation I get the feeling that I am making this way too complicated for myself also am I correct in thinking that as the electron showed cyclotronic motion that theta is 90 degrees? help please?

 

[mukundpa]

The magnetic force is behaving as centripetal force required to make the path circular.