Question

a beam of protons is sent in the positive x-direction (toward right) in a region with a uniform magnetic field B of 2 T in the positive z-direction (out of the page) and a uniform electric field E of 100 N/C. What should be the speed the protons and the direction of electric field so that protons are not deflected?

Answer 1

The protons should have a velocity of 100 m/s in the positive x-direction and the electric field should be in the negative x-direction with a magnitude of 100 N/C.

Step-by-step explanation:

The protons will not be deflected if the magnetic force and electric force are equal and opposite. The magnetic force on a proton moving in a magnetic field is given by the equation:

Fmagnetic = qvB

where q is the charge of the proton, v is the velocity of the proton, and B is the magnetic field.

The electric force on a proton moving in an electric field is given by the equation:

Felectric = qE

where E is the electric field.

To prevent deflection, the two forces must be equal:

qvB = qE

Since the charge of a proton is positive, the velocity and electric field must have opposite directions.

Therefore, the protons should have a velocity of 100 m/s in the positive x-direction (toward right) and the electric field should be in the negative x-direction (toward left) with a magnitude of 100 N/C.