Question

A charged particle carrying a charge \( q \) and moving with velocity \( v \), enters into a solenoid carrying a current \( I \), along its axis. If \( B \) is the magnetic induction along the axis of solenoid, then the force \( F \) acting on the charged particle will be

• A. \( F = 0 \)
• B. \( F = qvB \)
• C. \( F<qvB \)
• D. \( F>qvB \)

Hint:

When a charged particle moves parallel to the magnetic field, the force on it is zero because the angle between the velocity and the magnetic field is zero.

Answer 1

The Correct Option is A

Step 1: Understanding the force on a charged particle in a magnetic field.
The force on a charged particle moving with velocity \( v \) in a magnetic field \( B \) is given by the Lorentz force law: \[ F = qvB \sin \theta \] where \( \theta \) is the angle between the velocity vector and the magnetic field vector.
Step 2: Applying the condition in this case.
In this case, the charged particle enters the solenoid and moves along the axis of the solenoid. The magnetic field inside a solenoid is along its axis, and the velocity of the particle is also along the axis. Therefore, the angle \( \theta = 0^\circ \), and since \( \sin 0^\circ = 0 \), the force \( F = 0 \).
Step 3: Conclusion.
Thus, the force acting on the charged particle is zero, corresponding to option (A).