Question

Electron of mass m and charge $q$ is traveling with a speed along a circular path of radius $r$ at right angles to a uniform magnetic field of intensity B. If the speed of the electron is doubled and the magnetic field is halved the resulting path would have a radius.

• A. $2r$
• B. $4r$
• C. $\frac{r}{4}$
• D. $\frac{r}{2}$

Answer 1

Answer: (B)

$4r$

Radius of path is given by $r=\frac{mv}{Bq}$

Here, $m$ and $q$ remain unchanged

So, $\frac{r_1}{r_2}=\frac{v_1}{V_2}\cdot \frac{B_2}{B_1}=\frac{v}{2v}\cdot \frac{B/2}{B}=\frac{1}{4}$

$\Rightarrow r_2=4r$