Question

An ideal solenoid is kept with its axis vertical. Current \( I_0 \) is flowing in the solenoid. A charge \( Q \) is thrown downward inside the solenoid. If acceleration of the charge particle is \( a \), then

• A. \( a>g \)
• B. \( a = g \)
• C. \( a<g \)
• D. \( a = 0 \)

Hint:

When a charged particle moves in a uniform magnetic field with velocity parallel to the field, the magnetic force does not affect its motion. Gravity is the primary force acting on it.

Answer 1

The Correct Option is B

Step 1: Analyze the forces.
The magnetic force on a charged particle moving in a magnetic field is given by \( F_m = QvB \). Since the motion is downward, the charge experiences a force that will balance gravity in the vertical direction.
Step 2: Use the equation \( \vec{v} \parallel \vec{B} \) to understand the force.
From the equation \( \vec{v} \parallel \vec{B} \Rightarrow F_m = 0 \), we deduce that the acceleration of the charge particle is equal to gravity.
Step 3: Conclusion.
The acceleration of the charge particle inside the solenoid is equal to \( g \), which corresponds to option (2).