Four electric charges +q, +q, -q and -q are p | vedclass

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

Question

(C) Let the corners of the square be $P, Q, R, S$ in order. Let $P$ and $S$ have charges $+q$,and $Q$ and $R$ have charges $-q$. Point $A$ is the midp

Vedclass · Accepted Answer

$\frac{1}{4\pi \varepsilon_0} \frac{2q}{L} (1 - \frac{1}{\sqrt{5}})$

Vedclass · Answer

(C) Let the corners of the square be $P, Q, R, S$ in order. Let $P$ and $S$ have charges $+q$,and $Q$ and $R$ have charges $-q$. Point $A$ is the midpoint of side $PS$.Since the side length is $2L$,the distance from $A$ to $P$ and $A$ to $S$ is $L$.The distance from $A$ to $Q$ and $A$ to $R$ can be calculated using the Pythagorean theorem: $AQ = AR = \sqrt{(2L)^2 + L^2} = \sqrt{4L^2 + L^2} = L\sqrt{5}$.The electric potential $V_A$ at point $A$ is the algebraic sum of potentials due to all four charges:$V_A = \frac{1}{4\pi \varepsilon_0} [\frac{q}{AP} + \frac{q}{AS} + \frac{-q}{AQ} + \frac{-q}{AR}]$$V_A = \frac{1}{4\pi \varepsilon_0} [\frac{q}{L} + \frac{q}{L} - \frac{q}{L\sqrt{5}} - \frac{q}{L\sqrt{5}}]$$V_A = \frac{1}{4\pi \varepsilon_0} [\frac{2q}{L} - \frac{2q}{L\sqrt{5}}]$$V_A = \frac{1}{4\pi \varepsilon_0} \frac{2q}{L} (1 - \frac{1}{\sqrt{5}})$

Four electric charges $+q, +q, -q$ and $-q$ are placed at the corners of a square of side $2L$ (see figure). The electric potential at point $A$,midway between the two charges $+q$ and $+q$,is

Similar Questions

Two hollow conducting spheres of radii $R_{1}$ and $R_{2}$ $(R_{1} >> R_{2})$ have equal charges. The potential would be:

Assertion : Electric potential and electric potential energy are different quantities.
Reason : For a system of a positive test charge and a point charge,electric potential energy $=$ electric potential.

The electric potential of the Earth is taken to be zero because the Earth is a good:

Write an expression for the potential at a point outside a uniformly charged spherical shell,on the surface,and inside the shell.

Two identical metal balls of radius $r$ are at a distance $a$ $(a \gg r)$ from each other and are charged,one with potential $V_1$ and other with potential $V_2$. The charges $q_1$ and $q_2$ on these balls in $CGS$ $esu$ are

Vedclass Test Series

Exam Paper Generator

Online Exam Module