Question 957: Electrostats & Capacitance

Question

Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 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

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

8q1

Answer

6q1

Answer

8q2

Answer

6q2

Electrostats & Capacitance

Two charges q1 and q2 are placed 30 cm apart, as shown in the figure. A third charge q3 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

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