Question

Two protons enters a region of transverse magnetic
field with speed v and 2v. The ratio of respective
time period of revolution of protons is

Answer 1

Answer:

Ratio of time period will be  $\sqrt{2}:1$

Explanation:

We have given velocity of two proton is v and 2v

We know that force on proton in magnetic field is given by $F=qvB$

And centripetal force is given by $F=\frac{mv^2}{r}=m\omega ^2r$

These two force must equal

$m\omega ^2r=qvB$

$\omega =\sqrt{\frac{qvB}{mr}}$

We also know that $\omega =\frac{2\pi }{T}$

$\frac{2\pi }{T}=\sqrt{\frac{qvB}{mr}}$

From the relation we can see that $\frac{2\pi }{T}=\sqrt{\frac{qvB}{mr}}$

So ratio of time period will be  $\sqrt{2}:1$