Question

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 \(\frac{q_3K}{4\pi \in_0}\), the value of K is :

(1) \(8q_2\)

(2) \(6q_2\)

(3) \(8q_1\)

(4) \(6q_1\)

Answer 1

Correct option is : (1) \(8q_2\) 

\(u(C) = \left(\frac{kq_1}{40}+ \frac{kq_2}{50}\right)q_3\)

\(u(D) = \left(\frac{kq_1}{40}+ \frac{kq_2}{10}\right)q_3\)

So, \(\Delta u = |u(D)- u(C)| = kq_2\left[\frac{1}{10}- \frac{1}{50}\right]q_3\)

\(\Rightarrow \Delta u = \frac{kq_2 4}{50} q_3 = \frac{4q_2 q_3}{4 \pi \epsilon_0 50}\)

\(\Rightarrow \left(\frac{4 q_2 q_3 \times 2}{4 \pi \epsilon_0}\right)\) SI unit \(\iff \frac{q_3k}{4 \pi \epsilon_0}\)

\(\Rightarrow k = 8 q_2\)