First slide

Pontial due to

Question

A ring of radius I caries a charge +q. A test charge -q_o is released on its axis at a distance $\sqrt{3} R$ from its centre. How much kinetic energy will be acquired by the test charge when it reaches the centre of the ring ?

Moderate

A

$\frac{1}{4 {πε}_{0}} \times \frac{{qq}_{0}}{R}$
B

$\frac{1}{4 {πε}_{0}} \times \frac{{qq}_{0}}{2 R}$
C

$\frac{1}{4 {πε}_{0}} \times \frac{{qq}_{0}}{\sqrt{3} R}$
D

$\frac{1}{4 {πε}_{0}} \times \frac{{qq}_{0}}{3 R}$

Solution

Potential V₁, due to a ring is given by
$\begin{array}{l} V_{1} = \frac{1}{4 {πε}_{0}} \times \frac{q}{\sqrt{(R^{2} + r^{2})}} \\ = \frac{1}{4 {πε}_{0}} \times \frac{a}{\sqrt{R^{2} + 3 R^{2}}} (∵ r = \sqrt{3} R) \\ = \frac{1}{4 {πε}_{0}} \times \frac{q}{2 R} \end{array}$
At centre $V_{2} = \frac{1}{4 {πε}_{0}} \times \frac{q}{R}$
$K.E. = q_{0} (V_{2} - V_{1}) = \frac{1}{4 {πε}_{0}} (\frac{{qq}_{0}}{2 R})$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App