SATHEE: Electrostatics 7 Question 13

Electrostatics 7 Question 13

13. Two equal point charges are fixed at $x = - a$ and $x = + a$ on the $x$ -axis. Another point charge $Q$ is placed at the origin. The change in the electrical potential energy of $Q$ , when it is displaced by a small distance $x$ along the $x$ -axis, is approximately proportional to

$(2002, 1 M)$

(a) $x$

(b) $x^{2}$

(d) $1 / x$

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Answer:

Correct Answer: 13. (b)

Solution:

$\begin{aligned} U_{i} & = \frac{2 K Q q}{a} + \frac{K \cdot q \cdot q .}{2 a} \\ and U_{f} & = K Q q [\frac{1}{a + x} + \frac{1}{a - x}] + \frac{K \cdot q \cdot q .}{2 a} \end{aligned}$

$\begin{aligned} Here, K = \frac{1}{4 π ε_{0}} \\ Δ U = U_{f} - U_{i} \\ or | Δ U | = \frac{2 K Q q x^{2}}{a^{3}} \\ For x « a \\ ∴ Δ U \propto x^{2} \end{aligned}$

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Electrostatics 7 Question 13

13. Two equal point charges are fixed at x=−a and x=+a on the x-axis. Another point charge Q is placed at the origin. The change in the electrical potential energy of Q, when it is displaced by a small distance x along the x-axis, is approximately proportional to

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13. Two equal point charges are fixed at $x = - a$ and $x = + a$ on the $x$ -axis. Another point charge $Q$ is placed at the origin. The change in the electrical potential energy of $Q$ , when it is displaced by a small distance $x$ along the $x$ -axis, is approximately proportional to