Question

An electrically charged particle enters into a uniform magnetic induction field in a direction perpendicular to the field with a velocity $V$. Then, it travels:

• A. in a straight line without acceleration
• B. with force in the direction of the field
• C. in a circular path with a radius directly proportional to $V^2$
• D. in a circular path with a radius directly proportional to its velocity

Answer 1

Answer: (D)

in a circular path with a radius directly proportional to its velocity

When a charged particle enters into a uniform magnetic field in a direction perpendicular to field, then the particle traces a circular path.

The centripetal acceleration required to move in a circular path is provided by the magnetic force that the field exert on the particle.

$\therefore$ $F_{centripetal}=F_{magnetic}$

$\therefore$ $\frac{m{V}^2}{r}=qVB$

$⟹$ $r=\frac{mV}{Bq}$

Thus $r\propto V$