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A test charge q₀ moves into a magnetic field B aligned with the z-axis, traveling with velocity v̅ at an angle θ to the z-axis. The motion's time period does not depend on R or v. What can be said about the direction of the force acting on the charge?

1. The force acts in the same direction as the velocity.
2. The force is oriented at right angles to both the velocity and the magnetic field.
3. No force acts on the charge.
4. The force is aligned with the magnetic field's direction.

Correct answer: The force is oriented at right angles to both the velocity and the magnetic field.

Solution

The magnetic force on a charged particle moving in a magnetic field is given by the Lorentz force, F = q(v × B). This force is always perpendicular to both the velocity vector and the magnetic field, causing the particle to move in a circular or helical path.

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