Question

An ideal solenoid is kept with its axis vertical. A current \( I_0 \) is flowing in the solenoid. A charge \( q \) is thrown vertically downward inside the solenoid. The acceleration of the charged particle is:

• A. \( g \) downward
• B. \( g \) upward
• C. Zero
• D. Depends on the magnitude of current \( I_0 \)

Hint:

Important magnetic force facts:
Magnetic force acts only on the component of velocity perpendicular to \( \vec{B} \)
If \( \vec{v} \parallel \vec{B} \), magnetic force is zero
Gravity is unaffected by magnetic fields

Answer 1

The Correct Option is A

Step 1: In an ideal solenoid, the magnetic field inside is uniform and directed along the axis of the solenoid.
Step 2: The charged particle is thrown vertically downward, i.e., its velocity \( \vec{v} \) is parallel to the magnetic field \( \vec{B} \).
Step 3: Magnetic force on a moving charge is: \[ \vec{F} = q\,\vec{v} \times \vec{B} \] Since \( \vec{v} \parallel \vec{B} \), \[ \vec{v} \times \vec{B} = 0 \]
Step 4: Hence, no magnetic force acts on the particle. The only force acting is gravity. \[ \therefore \text{Acceleration of the particle} = g \text{ (downward)} \]