SATHEE: Electrostatic Potential and Capacitance

Electrostatic Potential and Capacitance - Result Question 17

19. Two charges $q_{1}$ and $q_{2}$ are placed $30 c m$ apart, as shown in the figure. A third charge $q_{3}$ is moved along the arc of a circle of radius $40 c m$ from $C$ to $D$ . The change in the potential energy of the system is $\frac{q_{3}}{4 π ϵ_{0}} k$ , where $k$ is

[2005]

(a) $8 q_{1}$

(b) $6 q_{1}$

(d) $6 q_{2}$

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Answer:

Correct Answer: 19. (c)

Solution:

$U = \frac{1}{4 π ϵ_{0}} (\frac{q_{1} q_{2}}{r_{12}} + \frac{q_{2} q_{3}}{r_{23}} + \frac{q_{3} q_{1}}{r_{31}})$

Here, $r_{12} = A B = 0.3 m, r_{31} = A C = 0.4 m$

According to question,

$\begin{aligned} U_{initial} & = \frac{1}{4 π ϵ_{0}} (\frac{q_{1} q_{2}}{0.3} + \frac{q_{2} q_{3}}{0.5} + \frac{q_{3} q_{1}}{0.4}) \\ r_{23} & = \sqrt{(0.3)^{2} + (0.4)^{2}} = 0.5 m \end{aligned}$

When the charge moved to point $D$

$r_{12} = 0.3 m$

$r_{23} = 0.1 m$

$r_{31} = 0.4 m$

$U_{final} = \frac{1}{4 π ϵ_{0}} (\frac{q_{1} q_{2}}{0.3} + \frac{q_{2} q_{3}}{0.1} + \frac{q_{3} q_{1}}{0.4})$

$U_{final} - U_{initial} = \frac{1}{4 π ϵ_{0}} (\frac{q_{1} q_{2}}{0.1} - \frac{q_{2} q_{3}}{0.5})$

$= \frac{1}{4 π ϵ_{0}} [10 q_{2} q_{3} - 2 q_{2} q_{3}] = \frac{q_{3}}{4 π ϵ_{0}} (8 q_{2})$

When we use the formula of potential energy of system of charges, then we consider that potential energy of the system at infinity is zero.

Electrostatic Potential and Capacitance - Result Question 17

19. Two charges $q_{1}$ and $q_{2}$ are placed $30 c m$ apart, as shown in the figure. A third charge $q_{3}$ is moved along the arc of a circle of radius $40 c m$ from $C$ to $D$ . The change in the potential energy of the system is $\frac{q_{3}}{4 π ϵ_{0}} k$ , where $k$ is

Answer:

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Electrostatic Potential and Capacitance - Result Question 17

19. Two charges q1 and q2 are placed 30cm apart, as shown in the figure. A third charge q3 is moved along the arc of a circle of radius 40cm from C to D. The change in the potential energy of the system is q34πϵ0k, where k is

Answer:

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19. Two charges $q_{1}$ and $q_{2}$ are placed $30 c m$ apart, as shown in the figure. A third charge $q_{3}$ is moved along the arc of a circle of radius $40 c m$ from $C$ to $D$ . The change in the potential energy of the system is $\frac{q_{3}}{4 π ϵ_{0}} k$ , where $k$ is