Question

A charged particle $-q_0$ is revolving around a fixed charge $+Q$ on a circular path at a constant speed. Identify the incorrect statement

• A. Change in momentum of a charged particle $-q_0$ is due to electrostatic force.
• B. Power delivered by electrostatic force is non-zero.
• C. Net acceleration of charge $-q_0$ is directed towards $+Q$.
• D. Charge $-q_0$ is not at equilibrium since its velocity is changing.

Answer 1

The correct option is B Power delivered by electrostatic force is non-zero.


Net acceleration of the particle in circular motion = Tangential acceleration $a_t$ + Centripetal acceleration $a_c$
Speed of the particle $\left(v\right)$ is constant, $a_t=0$
Centripetal acceleration of the charge is its net acceleration and always directed towards charge $+Q$ i.e. centre of circle
$a_c=\frac{v^2}{r}$
Here electrostatic force $F$ is providing necessary centripetal acceleration.
$\frac{kQ{q}_0}{r^2}=\frac{m{v}^2}{r}$
The electrostatic force is perpendicular to the velocity $\left(v^{\prime }\right)$ of the charge at each point on the path.
Thus power delivered by electrostatic force,
$P=\overrightarrow{F}.\overrightarrow{v^{\prime }}=0$

$\begin{array}{c}\text{Why this question ?}\\ \text{Tip: Change in K.E of particle is zero, thus}\\ W_{\text{electric force}}=0,\text{hence power delivered is also zero}\\ W_{\text{ext}}={\Delta }_{\text{K.E.}}\end{array}$