Question 773: Electrostatics & Capacitance

Question

Two charges q
1
and q
2
are placed 30 cm apart, as shown in the figure. A third charge q
3
is moved along the arc  of a circle of radius 40 cm from C to D.
The change in the potential energy of the system is ${{{q_3}} \over {4\pi {\varepsilon _0}}}$ where k is
![](https://neetcare-image.cdn.examgoal.net/1qpqdn5k7thq99f/177c2be4-d01c-4800-9b38-3b475d11270b/6830e240-66fb-11ea-997e-790b4402a570/file-1qpqdn5k7thq99g-350w.jpg)

Accepted Answer

We know that potential energy of discrete system of charges is given by
$U = {1 \over {4\pi {\varepsilon _0}}}\left( {{{{q_1}{q_2}} \over {{r_{12}}}} + {{{q_2}{q_3}} \over {{r_{23}}}} + {{{q_3}{q_1}} \over {{r_{31}}}}} \right)$
According to question,
${U_{initial}} = {1 \over {4\pi {\varepsilon _0}}}\left( {{{{q_1}{q_2}} \over {0.3}} + {{{q_2}{q_3}} \over {0.5}} + {{{q_3}{q_1}} \over {0.4}}} \right)$
${U_{final}} = {1 \over {4\pi {\varepsilon _0}}}\left( {{{{q_1}{q_2}} \over {0.3}} + {{{q_2}{q_3}} \over {0.1}} + {{{q_3}{q_1}} \over {0.4}}} \right)$
${U_{final}} - {U_{initial}} = {1 \over {4\pi {\varepsilon _0}}}\left( {{{{q_1}{q_2}} \over {0.1}} - {{{q_2}{q_3}} \over {0.5}}} \right)$
$ = {1 \over {4\pi {\varepsilon _0}}}\left[ {10{q_2}{q_3} - 2{q_2}{q_3}} \right] = {{{q_3}} \over {4\pi {\varepsilon _0}}}\left( {8{q_2}} \right)$

Answer

8q
1

Answer

6q
1

Answer

8q
2

Answer

6q
2

Electrostatics & Capacitance

Two charges q 1 and q 2 are placed 30 cm apart, as shown in the figure. A third charge q 3 is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is {{{q_3}} \over {4\pi {\varepsilon _0}}} where k is

Choose the correct answer: