Question

A particle of charge $q$ and mass $m$ is moving in a circle of radius $2r$ in a uniform magnetic field of strength $B$.
Which of the following is a correct relationship for the magnitude of an Electric Field $E$ that would cause the charge to move in a straight line at a constant speed?

• A. $vB$
• B. $E=\frac{rq{B}^2}{m}$
• C. $E=\frac{2rq{B}^2}{m}$
• D. $E=\frac{rq{B}^2}{2m}$
• E. $E=\frac{2rqB}{m}$

Answer 1

Answer: (C)

$E=\frac{2rq{B}^2}{m}$

Radius of circular path $R=2r$

Using $BqR=mv$

$\therefore$ $Bq\left(2r\right)=mv$ $⟹v=\frac{2rqB}{m}$

Thus magnitude of electric field $E=vB=\frac{2rq{B}^2}{m}$