Answer to Question #95010 in Electricity and Magnetism for vanessa abou samra

Question

A particle of mass

Answer 1

Sometimes problems like that start like this:

A particle of mass 0.001 g and charge 0.03 C hits a region with magnetic field of 16 T directed perpendicularly to the particle's velocity vector. What velocity did the particle have if the radius of the trajectory was 98 cm?

I took absolutely random numbers from my head. The solution is below.

Since the charged particle moves in magnetic field, Lorenz force influenced the particle's motion. The magnitude of the Lorenz force:

$$F_L=qvB.$$

At the same time, since the particle has inertia (mass), there is a centripetal force acting on the particle as well:

$$F_C=ma=m\frac{v^2}{R}.$$

And these two forces are in equilibrium while the particle moves along a circle:

$$qvB=m\frac{v^2}{R},\\ \space\\ v=\frac{qBR}{m}=470400\text{ m/s}.$$

Quite fast, but still quite far from the speed of light.