Question

A particle having charge \( +q \) enters a uniform magnetic field \( \vec{B} \) as shown in the figure. The particle will describe:

• A. a circular path in XZ plane
• B. a semicircular path in XY plane
• C. a helical path with its axis parallel to Y-axis
• D. a semicircular path in YZ plane

Hint:

Use the right-hand rule on \( \vec{v} \times \vec{B} \) to determine the direction of force on a positively charged particle. If \( \vec{v} \perp \vec{B} \), motion is circular in the plane defined by those two vectors.

Answer 1

The Correct Option is B

From the figure, the particle has an initial velocity along the positive Y-axis, and the magnetic field \( \vec{B} \) is directed into the plane of the paper (denoted by crosses).
The magnetic force on a moving charged particle is given by the Lorentz force: \[ \vec{F} = q\vec{v} \times \vec{B} \] - Here, \( \vec{v} \) is along \( +Y \) and \( \vec{B} \) is into the page (\( -Z \)). - Using the right-hand rule for \( \vec{v} \times \vec{B} \), the force \( \vec{F} \) acts along the \( +X \) direction. - This force acts as the centripetal force, causing the charged particle to undergo circular motion in the XY plane.
Since the particle enters perpendicularly and no velocity component exists along the magnetic field, the motion is confined to the plane. The particle describes a semicircular path before possibly exiting the field region. Final answer: Semicircular path in XY plane