Question

Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius R with constant speed v. The time period of the motion

• A. depends on both R and v
• B. is independent of both R and v
• C. depends on R and not v
• D. depends on v and not on R

Answer 1

The correct option is B is independent of both R and v

In a uniform magnetic field, a charged particle is moving in a circle of radius R with constant speed v.

$\therefore \frac{m{v}^2}{R}=Bqv$ or $R=\frac{mv}{Bq}$ .......... (1)

Time period, $T=\frac{2\pi R}{v}=\frac{2\pi mv}{Bqv}=\frac{2\pi m}{Bq}$ ......... (2)

Time period T does not depend on both R and v because v is changed, R is also changed proportionately and for period, it is R/v that is taken.