A charged particle moving along the x-axis enters a uniform magnetic field pointing along the z-axis. A uniform electric field is also present. Due to the combined effect of both fields, the particle does not change its velocity. What is the direction of the electric field

Positive y-axis

Explanation:

First of all, we need to find the direction of the magnetic force.

We know that the direction of the magnetic force on a charged moving particles is perpendicular to both the velocity of the particle and the direction of the magnetic field. For a positive charged particle, we can use the right-hand rule. In this case, we find:

- index finger: direction of the velocity of the particle (positive x-axis)

- middle finger: direction of the magnetic field (positive z-axis)

- thumb: direction of the magnetic force (in this case, negative y-axis)

Therefore, the direction of the magnetic force is in the negative y-axis.

In order for the particle to not change its velocity (so, being undeflected), the electric force must balance the magnetic force: therefore, the electric force must be in the opposite direction as the magnetic force, so in the

positive y-axis

direction.

We also know that for a positively charged particle ,the direction of the electric force is the same as the electric field: therefore, the direction of the electric field is also along the positive y-axis.

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