Question

A particle of charge q enters a region of uniform magnetic field \(\vec B\) (pointing into the page). The field deflects the particle a distance d above the original line of flight, as shown in below figure. Is the charge positive or negative ? Find the momentum of the particle in terms of a, d, B and q.

Answer 1

Since \(\vec v\) x \(\vec B\) points upward, and that is also the direction of the magnetic force \(\vec F_m\), q must be positive.

Using the Pythagorean theorem to find R in terms of a and d,

(R - d)² + a² = R² so that 

R = \(\cfrac{a^2+d^2}{2d}\)

Then, from the cyclotron formula, the momentum of the charged

Particle is p = |q| BR = |q|B \(\left(\cfrac{a^2+d^2}{2d}\right)\)