Electrostatics Ques 3
- A positive point charge $q$ is fixed at origin. A dipole with a dipole moment pis placed along the $x$-axis far away from the origin with $\mathbf{p}$ pointing along positive $x$-axis. Find : (a) the kinetic energy of the dipole when it reaches a distance $d$ from the origin, and (b) the force experienced by the charge $q$ at this moment.
$(2003,4 M)$
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Answer:
Correct Answer: 3.(a) $\mathrm{KE}=\frac{q p}{4 \pi \varepsilon_0 d^2}$ (b) $\mathbf{F}=\frac{p q}{2 \pi \varepsilon_0 d^3} \hat{\mathbf{i}}$)
Solution:
- (a) Applying energy conservation principle, increase in kinetic energy of the dipole $=$ decrease in electrostatic potential energy of the dipole.
$\therefore$ Kinetic energy of dipole at distance $d$ from origin
$ =U_i-U_f $
$ \begin{aligned} or \quad \mathrm{KE} & =0-(-\mathbf{p} \cdot \mathbf{E})=\mathbf{p} \cdot \mathbf{E} \ & =(p \hat{\mathbf{i}}) \cdot\left(\frac{1}{4 \pi \varepsilon_0} \frac{q}{d^2} \hat{\mathbf{i}}\right)=\frac{q p}{4 \pi \varepsilon_0 d^2} \end{aligned} $
(b) Electric field at origin due to the dipole,
$ \mathbf{E}=\frac{1}{4 \pi \varepsilon_0} \frac{2 p}{d^3} \hat{\mathbf{i}}\left(\mathbf{E}_{\text {auis }} \uparrow \uparrow \mathbf{p}\right) $
$\therefore$ Force on charge $q$
$ \mathbf{F}=q \mathbf{E}=\frac{p q}{2 \pi \varepsilon_0 d^3} \hat{\mathbf{i}} $
BETA
