Protons in magnetic fields

Question

A beam of protons is directed in a straight line along the +z direction through a region of space in which there are crossed electric and magnetic fields. The electric field is 500 V/m in the -y direction and the protons move at a constant speed of 10^5 m/s.

What must be the magnitude of the magnetic field such that the beam of protons continues along its straight-line trajectory?

Answer 1

Hello Annie!

Crossed electric and magnetic fields means that they are perpendicular to one another. For the protons to move in a straight line at a constant velocity, the magnitude of the electric force from the field and the magnetic field must be equal (but opposite in direction).

F(electric) = F(magnetic)

qE = qvB

E = vB

B = E/v = (500 V/m) / 10⁵ m/s

B = 5 x 10^-3 V s / m² = 5 x 10^-3 Tesla