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...which direction?

Negative z-direction

Explanation:

The direction of the force exerted by the magnetic field on a moving (positive) charged particle can be found by using the right-hand rule:

- The index finger corresponds to the direction of the velocity of the particle

- The middle finger corresponds to the direction of the magnetic field

- The thumb gives the direction of the force

For the proton in this problem:

- Index finger: positive x-direction (direction of the velocity)

- Middle finger: positive y-direction (direction of magnetic field)

- Thumb: positive z-direction (direction of the force)

So, the magnetic force on the proton acts in the positive z-direction.

The electric force on a positive charged particle, instead, has the same direction as the electric field.

In this problem, in order to balance the magnetic force, we have to apply an electric force in the negative z-direction: therefore, the electric field must be in the negative z-direction as well, so that the proton will continue along a straight line.