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 q34πε0k, where k is

u1=14πε0q1q230 x 10-2+q1q340 x 10-2+q2q350 x 10-2u2=14πε0q1q230 x 10-2+q1q340 x 10-2+q2q310 x 10-2∆u=u2-u1=q2q34πε0 x 102110-150 =q2q34πε0 x 450 x 100=q34πε08q2 ∴k=8q2

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 q34πε0k, where k is

u1=14πε0q1q230 x 10-2+q1q340 x 10-2+q2q350 x 10-2u2=14πε0q1q230 x 10-2+q1q340 x 10-2+q2q310 x 10-2∆u=u2-u1=q2q34πε0 x 102110-150 =q2q34πε0 x 450 x 100=q34πε08q2 ∴k=8q2

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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 $\frac{q_{3}}{4 {πε}_{0}} k$ , where k is

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8q₂

8q₁

6q₂

6q₁

answer is A.

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Detailed Solution

$\begin{array}{rcl} u_{1} & = & \frac{1}{4 {πε}_{0}} [\frac{q_{1} q_{2}}{30 x 10^{- 2}} + \frac{q_{1} q_{3}}{40 x 10^{- 2}} + \frac{q_{2} q_{3}}{50 x 10^{- 2}}] \\ u_{2} & = & \frac{1}{4 {πε}_{0}} [\frac{q_{1} q_{2}}{30 x 10^{- 2}} + \frac{q_{1} q_{3}}{40 x 10^{- 2}} + \frac{q_{2} q_{3}}{10 x 10^{- 2}}] \\ ∆ u & = & u_{2} - u_{1} = \frac{q_{2} q_{3}}{4 {πε}_{0}} x 10^{2} [\frac{1}{10} - \frac{1}{50}] \\ = & \frac{q_{2} q_{3}}{4 {πε}_{0}} x \frac{4}{50} x 100 = \frac{q_{3}}{4 {πε}_{0}} (8 q_{2}) ∴ k = 8 q_{2} \end{array}$