A proton with a velocity in the positive x-direction enters a region where there is a uniform magnetic field B in the positive y-direction. You want to balance the magnetic force with an electric force so that the proton will continue along a straight line. The electric field should be in the:

- positive x-direction

- positive z-direction

- negative y-direction

- negative x-direction

- negative z-direction

- negative z-direction

Explanation:

First of all, we have to determine the direction of the magnetic force acting on the proton.

The direction of the magnetic force acting on a moving charge can be determined by using the right hand rule. For a positively charged particle:

- Index finger: direction of the motion of the particle

- Middle finger: direction of the magnetic field

- Thumb: direction of the force

For a negatively charged particle, the direction of the thumb must be reversed.

In this problem, we have a proton (positive charge), and we have:

- Direction of motion: positive x

- Direction of the field: positive y

Therefore, by using the right-hand rule, we see that the thumb points towards z-positive direction: so, this is the direction of the magnetic force.

Therefore, the proton is deviated towards z-positive direction due to the magnetic force; in order to balance this and make the proton continuing along a straight line, the electric force must be in the z-negative direction.

The electric force experienced by a charged particle has the same direction of the electric field (if the charge is positive) or opposite direction (if the charge is negative): in this problem, the proton is positive, so the direction of the electric field must be the same of the force, therefore

-  negative z-direction