A particle of charge $q$ and mass $m$ enters normally (at point $P$ ) in a region of magnetic field with speed $v$ . It comes out normally from $Q$ after time $T$ as shown in figure. The magnetic field B is present only in the region of radius R and is uniform. Initial and final velocities are along radial direction and they are perpendicular to each other. For this to happen, which of the following expression(s) is/are correct?

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$B = \frac{m v}{q R}$

$T = \frac{π R}{2 v}$

$T = \frac{π m}{2 q B}$

None of these

answer is A, B, C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

The particle will move along an arc which is part of a circle of radius:
$r = \frac{m v}{B q}$
From figure, we can see that $r = R$
$∴ R = \frac{m v}{B q}$
$T = \frac{π r / 2}{v} = \frac{π r}{2 v} = \frac{π R}{2 v} (∵ r = R = \frac{m v}{B q})$
$∴ T = \frac{π m}{2 B q}$
Question Image