Question

A charge \( q \) enters with speed \( v \) in the direction of magnetic field \( B \). The force on the charge in magnetic field will be:

• A. \( \dfrac{qvB}{2} \)
• B. \( qvB \)
• C. \( 2qvB \)
• D. zero

Hint:

Remember that the force on a moving charge in a magnetic field depends on the angle between the velocity and magnetic field. If they are in the same direction, the force is zero.

Answer 1

The Correct Option is D

The magnetic force on a moving charge is given by the equation \[ F = qvB \sin \theta \] where: - \( q \) is the charge,
- \( v \) is the velocity of the charge,
- \( B \) is the magnetic field, and
- \( \theta \) is the angle between the velocity vector and the magnetic field vector.
When the charge enters the magnetic field in the same direction as the magnetic field lines, the angle between the velocity and magnetic field becomes \( \theta = 0^\circ \). The sine of \( 0^\circ \) is zero, so the force on the charge becomes: \[ F = qvB \sin 0^\circ = 0 \] Therefore, the magnetic force on the charge in this situation is zero, and the correct answer is option (D).