Two charges and are separated by a distance of 30 cm. A third charge initially at 'C' as shown in the figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of from C to D is given b

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Solution

Q.
Two charges $q_{1}$ and $q_{2}$ are separated by a distance of 30 cm. A third charge $q_{3}$ initially at 'C' as shown in the figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of $q_{3}$ from C to D is given by $\frac{q_{3} K}{4 π ε_{0}}$ , the value of K is: [2025]

1 $8 q_{2}$

2 $6 q_{2}$

3 $8 q_{1}$

4 $6 q_{1}$

Ans.
(1)

Potential at C, $V_{C} = \frac{k q_{1}}{0.4} + \frac{k q_{2}}{0.5}$

Potential at D, $V_{D} = \frac{k q_{1}}{0.4} + \frac{k q_{2}}{0.1}$

The difference in potential energy,

$△ U = (V_{D} - V_{C}) (q_{3}) = (\frac{k q_{2}}{0.1} - \frac{k q_{2}}{0.5}) (q_{3})$

$△ U = 8 k q_{2} q_{3} = \frac{8 q_{2} q_{3}}{4 π ε_{0}}$

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