Consider the configuration of a system of fou | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) The work done by an external agent is given by $W_{ext} = U_f - U_i$.In Figure $(1)$,the charges are at the corners of a square of side $a$. The p

Vedclass · Accepted Answer

$\frac{-kq^2}{a}(3 - \sqrt{2})$

Vedclass · Answer

(D) The work done by an external agent is given by $W_{ext} = U_f - U_i$.In Figure $(1)$,the charges are at the corners of a square of side $a$. The potential energy $U_i$ is the sum of the potential energies of all pairs:$U_i = 4 	imes \frac{kq^2}{a} + 2 	imes \frac{kq^2}{a\sqrt{2}} = \frac{kq^2}{a}(4 + \sqrt{2})$.In Figure $(2)$,the charges are at the corners of a square inscribed in a circle of radius $a$. The distance between adjacent charges is $a\sqrt{2}$ and the distance between opposite charges is $2a$. The potential energy $U_f$ is:$U_f = 4 	imes \frac{kq^2}{a\sqrt{2}} + 2 	imes \frac{kq^2}{2a} = \frac{kq^2}{a}(2\sqrt{2} + 1)$.Now,calculate the work done:$W_{ext} = U_f - U_i = \frac{kq^2}{a} [(2\sqrt{2} + 1) - (4 + \sqrt{2})]$$W_{ext} = \frac{kq^2}{a} (\sqrt{2} - 3) = -\frac{kq^2}{a} (3 - \sqrt{2})$.

Consider the configuration of a system of four charges each of value $+q$. The work done by an external agent in changing the configuration of the system from Figure $(1)$ to Figure $(2)$ is:

Similar Questions

The electric potential at a distance of $3 \, m$ on the axis of a short dipole of dipole moment $4 \times 10^{-12} \, C \cdot m$ is ......... $mV$.

Two equal charges of magnitude $Q$ each are placed at a distance $d$ apart. Their electrostatic energy is $E$. $A$ third charge $-Q / 2$ is brought midway between these two charges. The electrostatic energy of the system is now

Three point charges $3 \text{ nC}$,$6 \text{ nC}$,and $9 \text{ nC}$ are placed at the corners of an equilateral triangle of side $0.1 \text{ m}$. The potential energy of the system is:

The work done required to assemble the four charges at the corners of a square of side $a$, as shown in the figure, is:

When one electron is moved towards another electron,the electric potential energy of the system:

Vedclass Test Series

Exam Paper Generator

Online Exam Module