Question

A charged particle enters perpendicular to a uniform magnetic field. The path followed by the particle is:

• A. Straight line
• B. Parabolic
• C. Circular
• D. Elliptical

Hint:

If velocity is perpendicular to magnetic field: \[ \vec v \perp \vec B \] the particle performs uniform circular motion.

Answer 1

The Correct Option is C

Concept: When a charged particle moves perpendicular to a magnetic field, magnetic force acts as centripetal force. Magnetic force: \[ F=qvB\sin\theta \] For perpendicular motion: \[ \theta=90^\circ \] thus: \[ F=qvB \]

Step 1: Identify direction of force. Magnetic force is always perpendicular to velocity. Therefore it changes direction of velocity but not speed.

Step 2: Compare with centripetal force. For circular motion: \[ \frac{mv^2}{r}=qvB \] Hence: \[ r=\frac{mv}{qB} \] Thus particle moves in a circular path.

Step 3: Final answer. \[ \boxed{ \text{Circular path} } \]