Charges Q are placed at each corner of a squa | vedclass

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

Question

(C) The work required to move a charge $q$ from a point with potential $V_0$ to infinity is given by $W = q(V_{\infty} - V_0)$. Since $V_{\infty} = 0$

Vedclass · Accepted Answer

$\frac{\sqrt{2} Q^2}{\pi \varepsilon_0 a}$

Vedclass · Answer

(C) The work required to move a charge $q$ from a point with potential $V_0$ to infinity is given by $W = q(V_{\infty} - V_0)$. Since $V_{\infty} = 0$,the work required is $W = -qV_0$. Here,$q = -Q$,so $W = -(-Q)V_0 = QV_0$.The potential $V_0$ at the center of the square due to the four charges $Q$ at the corners is the sum of the potentials due to each charge.The distance from each corner to the center is $r = \frac{a}{\sqrt{2}}$.$V_0 = 4 	imes \left( \frac{1}{4\pi \varepsilon_0} \cdot \frac{Q}{a/\sqrt{2}} ight) = \frac{4\sqrt{2} Q}{4\pi \varepsilon_0 a} = \frac{\sqrt{2} Q}{\pi \varepsilon_0 a}$.Therefore,the work required is $W = (-Q) 	imes (-V_0) = Q 	imes \left( \frac{\sqrt{2} Q}{\pi \varepsilon_0 a} ight) = \frac{\sqrt{2} Q^2}{\pi \varepsilon_0 a}$.

Charges $Q$ are placed at each corner of a square of side $a$. How much work is required to remove a charge $-Q$ from the center of the square and move it to infinity?

Similar Questions

Two equal positive charges each of value $q$ are placed at points $A$ and $B$, where $AB = 3x$. A third charge $-3q$ is placed at point $C$ at a distance $x$ from $A$ on the line segment $AB$. The potential energy of the system is nearly ($\epsilon_0$ = permittivity of free space).

$1\,eV$ is

Eight identical charged drops combine to form a single large drop. If the potential of each small drop is $10 \ V$,then the potential of the large drop will be ........ $V$?

Along the $x$-axis,three charges $\frac{q}{2}, -q$ and $\frac{q}{2}$ are placed at $x=0, x=a$ and $x=2a$ respectively. The resultant electric potential at a point $P$ located at a distance $r$ from the charge $-q$ $(r > a)$ is ($\varepsilon_0$ is the permittivity of free space):

Vedclass Test Series

Exam Paper Generator

Online Exam Module