Question

A particle of mass $M$ and charge $Q$ moving with velocity $\overrightarrow{v}$ describe a circular path of radius $R$ when subjected to a uniform transverse magnetic field of induction $B$. The work done by the field when the particle completes one full circle is:

• A. $\left(\frac{{Mv}^2}{R}\right)2\pi R$
• B. zero
• C. $BQ2\pi R$
• D. $BQv2\pi R$

Answer 1

The correct option is B zero

Force= $\overrightarrow{F}=Q(\overrightarrow{\nu }\times \overrightarrow{B})$

$\therefore$ Work done= $W=\overrightarrow{F}d\overrightarrow{r}$

$=Q(\overrightarrow{\nu }\times \overrightarrow{B})d\overrightarrow{r}$

$=0$ $[\because \text{Angle between}(\overrightarrow{\nu }\times \overrightarrow{B}\left)\text{and}d\overrightarrow{r}\text{is}\pi /2\right]$