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

To determine the acceleration of the charged particle moving through an ideal solenoid, we must consider the forces at play.

1. First, recognize that an ideal solenoid produces a uniform magnetic field inside it along the direction of its axis. The direction of the magnetic field within the solenoid is along the line of the solenoid.
2. The force acting on a charged particle in a magnetic field is given by the Lorentz force formula: \(F = q(\mathbf{v} \times \mathbf{B})\), where \(q\) is the charge, \(\mathbf{v}\) is the velocity, and \(\mathbf{B}\) is the magnetic field. 
3. In this scenario, the particle is thrown vertically downward, and the magnetic field inside the solenoid is also vertical (along the solenoid's axis). Therefore, the velocity vector and the magnetic field vector are parallel.
4. When vectors are parallel, the cross-product is zero: \(\mathbf{v} \times \mathbf{B} = 0\). This means the magnetic force on the particle is zero.
5. Since the only other force acting on the particle is gravity, the net force is only due to gravity. Hence, the only acceleration experienced by the charged particle is due to gravity, which points downward.

Therefore, the acceleration of the charged particle is \(g\) downward.

Conclusion: The correct answer is "

\( g \) downward

". The magnetic field inside the solenoid does not exert any magnetic force on the particle because its velocity is parallel to the field.