Question:

Two positive charges of magnitude $'q'$ are placed at the ends of a side (side 1) of a square of side $'2a'$. Two negative charges of the same magnitude are kept at the other corners. Starting from rest, if a charge $Q$ moves from the middle of side $1$ to the centre of square, its kinetic energy at the centre of square is :

Updated On: Jul 31, 2023
  • zero
  • $\frac{1}{4\pi\varepsilon_{0}} \frac{2qQ}{a}\left(1+\frac{1}{\sqrt{5}}\right)$
  • $\frac{1}{4\pi\varepsilon_{0}} \frac{2qQ}{a}\left(1-\frac{2}{\sqrt{5}}\right)$
  • $\frac{1}{4\pi\varepsilon_{0}} \frac{2qQ}{a}\left(1-\frac{1}{\sqrt{5}}\right)$
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The Correct Option is D

Solution and Explanation

Potential at point A, $V_{A} = \frac{2kq}{a}- \frac{2ka}{a\sqrt{5}}$ Potential at point B, $V_{B} = 0$ $\therefore\quad$ Using work energy theroem $W_{AB )\,electric} = Q\left(V_{A} - V_{B}\right)$ $=\quad \frac{2KqQ}{a}\left[1-\frac{1}{\sqrt{5}}\right]\quad\quad=\quad\left( \frac{1}{4\pi\varepsilon_{0}}\right) \frac{2Qq}{a}\left[1-\frac{1}{\sqrt{5}}\right]$

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Concepts Used:

Electrostatic Potential and Capacitance

Electrostatic Potential

The potential of a point is defined as the work done per unit charge that results in bringing a charge from infinity to a certain point.

Some major things that we should know about electric potential:

  • They are denoted by V and are a scalar quantity.
  • It is measured in volts.

Capacitance

The ability of a capacitor of holding the energy in form of an electric charge is defined as capacitance. Similarly, we can also say that capacitance is the storing ability of capacitors, and the unit in which they are measured is “farads”.

Read More: Electrostatic Potential and Capacitance

The capacitor is in Series and in Parallel as defined below;

In Series

Both the Capacitors C1 and C2 can easily get connected in series. When the capacitors are connected in series then the total capacitance that is Ctotal is less than any one of the capacitor’s capacitance.

In Parallel

Both Capacitor C1 and C2 are connected in parallel. When the capacitors are connected parallelly then the total capacitance that is Ctotal is any one of the capacitor’s capacitance.