Aproton traveling at 27.1° with respect to the direction of a magnetic field of strength 2.33 mt experiences a magnetic force of 6.54 × 10-17 n. calculate (a) the proton's speed and (b) its kinetic energy in electron-volts.

(a) The magnetic force experienced by a charged particle is:

where
q is the charge
v is the velocity of the particle
B is the magnitude of the magnetic field
is the angle between the directions of v and B

The proton in our problem has a charge of , and it travels through a magnetic field with strength 

The direction between its velocity and B is , and the force exerted on the proton is . Re-arranging the previous equation and using these data, we can find the value of v:


(b) Using the mass of the proton, , we find its kinetic energy:


And keeping in mind that , we can convert this value into electronvolts: