Aproton moves at a speed of 2.0 x 10^7 m/s at right angles to a magnetic field that is directed into the page with a magnitude of 0.1t, calculate the radius of the orbit

The Lorentz force acting on the proton is equal to:

where
q is the proton charge
v is the proton speed
B is the intensity of the magnetic field
is the angle between the direction of v and B

since the proton travels perpendicularly to the magnetic field, in this case , so the Lorentz force in this case is simply


The magnetic force provides also the centripetal force that keeps the proton in circular motion:

where 
m is the proton mas
r is the radius of the orbit

If we re-arrange this equation and we use the data of the problem, we can find the radius of the orbit: