Question

Which of the following relations is correct?

• A. $r=\frac{mv}{qB}$
• B. $r=\frac{qB}{mv}$
• C. $r=\frac{mq}{vB}$
• D. $r=\frac{mB}{qv}$

Answer 1

The correct option is A $r=\frac{mv}{qB}$

When a charged particle of charge q and mass m is projected with velocity v in a uniform magnetic field B perpendicularly, then it moves in a circular path of radius r.
Now, Centripetal force = Magnetic force
$\Rightarrow \frac{m{v}^2}{r}=qvB$
$\Rightarrow r=\frac{mv}{qB}$
Hence, the correct answer is option (1).