Question

If a charged particle enters a uniform magnetic field \( B \), with a velocity \( v \) such that \( v \) has a component along \( B \), then the charged particle describes:

• A. A circular path
• B. An elliptical path
• C. A straight line
• D. A helical path
• E. A parabolic path

Hint:

When a charged particle has a component of velocity along the magnetic field, it follows a helical path, with the motion perpendicular to the magnetic field forming a circle, and the parallel component causing linear motion along the field.

Answer 1

The Correct Option is D

When a charged particle enters a magnetic field, the motion of the particle is influenced by the Lorentz force, which is given by:

\[ F = q(\mathbf{v} \times \mathbf{B}) \]

Where:

• \( q \) is the charge of the particle,
• \( \mathbf{v} \) is the velocity of the particle,
• \( \mathbf{B} \) is the magnetic field.

The force \( F \) is perpendicular to the velocity \( \mathbf{v} \), so the particle will follow a circular path due to the magnetic force. However, when the velocity \( \mathbf{v} \) has a component along the magnetic field \( \mathbf{B} \), this component of the velocity does not experience any magnetic force because the magnetic force is perpendicular to both the velocity and the magnetic field.

Thus, the particle will:

• Move in a circular path due to the component of velocity perpendicular to \( \mathbf{B} \).
• Move in a straight line along the direction of the component of velocity parallel to \( \mathbf{B} \).

The combination of these two motions results in a helical path.

Therefore, the correct answer is:

\[ \boxed{\text{D) A helical path}} \]