Auniform magnetic field points upward, parallel to the page, and has a magnitude of 7.85 mt. a negatively charged particle (q=−3.32 μc, m=2.05 pg) moves through this field with a speed of 67.3 km/s perpendicular to the magnetic field, as shown. the magnetic force on this particle is a centripetal force and causes the particle to move in a circular path. what is the radius of the particle's circular path?

The Lorentz force exerted on the particle due to the magnetic field provides the centripetal force that keeps the particle in circular motion:

where
m is the particle mass
v is its velocity
r its orbital radius
q its charge
B the magnetic field intensity
and where we neglected the factor  in the Lorentz force formula because the particle is traveling perpendicular to the magnetic field, so  .

Re-arranging the formula, we get
(1)
The problem gives us all the data about the particle and the magnetic field:


(we are only interested in the magnitude of the charge)


And by plugging these numbers into eq.(1), we find the radius of the orbit