Question

A proton, moving in a uniform magnetic field, moves in a circle perpendicular to the field lines and takes time T for each circle. If the proton's speed tripled, what would now be its time to go around each circle? 42) A) 9T B) T C) 3T D) T/9 E) T/3 Answer: B

Answer 1

Answer:

option (B)

Explanation:

mass of proton, m = m

charge of proton, q = e

Time period, T = T

Initially the speed of proton is v.

The time period of the proton when it is moving in magnetic field perpendicular to the direction of magnetic field is given by

$T=\frac{2\pi r}{v}$

Where, r be the radius of circular path.

The relation between r and the speed v is given by

$r=\frac{mv}{Bq}$

Where, B be the strength of magnetic field. Substitute this value of r in the expression of time period

$T=\frac{2\pi mv}{Bqv}=\frac{2\pi m}{Bq}$

Here, we observe that the expression for the time period is independent to v and r so, as we change the velocity, the time period remains same.