Question

An electron is projected along the axis of solenoid which carries constant current i, the trajectory of electron shall be

• A. Circular path
• B. Uniform motion along the axis
• C. Uniform accelerated motion in straight line
• D. Parabolic path

Answer 1

The Correct Option is B

An electron is projected along the axis of a solenoid which carries a constant current, and the question is about determining its trajectory. Let us analyze this situation step by step.

1. Understanding the Magnetic Field inside a Solenoid:
   • A solenoid is a coil of wire designed to create a magnetic field along its axis when a current flows through it.
   • The magnetic field inside a long solenoid is uniform and parallel to its axis. Its magnitude is given by the formula: B = \mu_0 n i, where B is the magnetic field, \mu_0 is the permeability of free space, n is the number of turns per unit length, and i is the current through the solenoid.
2. Magnetic Force on a Moving Electron:
   • According to the Lorentz force law, a charged particle like an electron experiences a force \mathbf{F} = q(\mathbf{v} \times \mathbf{B}) when moving in a magnetic field, where q is the charge, \mathbf{v} is the velocity, and \mathbf{B} is the magnetic field.
   • Since the electron is moving along the axis of the solenoid, the velocity vector \mathbf{v} is parallel to the magnetic field vector \mathbf{B}.
   • This means that the angle \theta between \mathbf{v} and \mathbf{B} is zero.
   • Since the cross product of two parallel vectors is zero, the force experienced by the electron is zero: \mathbf{F} = qvB\sin(\theta) = 0.
3. Conclusion on Electron's Motion:
   • With no magnetic force acting on it, and assuming no other forces are acting on the electron (like electric fields or frictional forces), it will continue its motion as per Newton's first law of motion.
   • This means the electron will travel with uniform motion along the axis of the solenoid.
4. Elimination of Other Options:
   • Circular Path: This would require a perpendicular component of velocity to the magnetic field, which is not the case here, hence incorrect.
   • Uniform Accelerated Motion in Straight Line: Accelerated motion implies a change in velocity due to a force, but as explained, the force is zero, hence incorrect.
   • Parabolic Path: This requires an additional acceleration component such as gravity or an electrostatic field, which is absent in this case, hence incorrect.

Therefore, the correct answer is: Uniform motion along the axis.