Four charges,each of value Q = frac{10}{3} ti | vedclass

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

Question

(D) The electric potential $V$ at the center of a square due to four identical charges $Q$ at its corners is given by the sum of potentials due to eac

Vedclass · Accepted Answer

$1500\sqrt{2} \ V$

Vedclass · Answer

(D) The electric potential $V$ at the center of a square due to four identical charges $Q$ at its corners is given by the sum of potentials due to each charge.Each charge is at a distance $r$ from the center,where $r$ is half the diagonal of the square.Diagonal of the square $= a\sqrt{2}$.So,$r = \frac{a\sqrt{2}}{2} = \frac{a}{\sqrt{2}}$.The potential at the center is $V = 4 	imes \frac{kQ}{r} = 4 	imes \frac{kQ}{a/\sqrt{2}} = \frac{4\sqrt{2}kQ}{a}$.Given $Q = \frac{10}{3} 	imes 10^{-9} \ C$,$a = 8 	imes 10^{-2} \ m$,and $k = 9 	imes 10^9 \ N \cdot m^2/C^2$.$V = \frac{4 	imes \sqrt{2} 	imes 9 	imes 10^9 	imes (\frac{10}{3} 	imes 10^{-9})}{8 	imes 10^{-2}}$.$V = \frac{4 	imes \sqrt{2} 	imes 3 	imes 10}{8 	imes 10^{-2}} = \frac{120\sqrt{2}}{8 	imes 10^{-2}} = 15 	imes 10^2 \sqrt{2} = 1500\sqrt{2} \ V$.

Four charges,each of value $Q = \frac{10}{3} \times 10^{-9} \ C$,are placed at the four corners of a square of side $a = 8 \ cm$. What is the electric potential at the center of the square?

Similar Questions

Four electric charges $+q, +q, -q$ and $-q$ are placed in order at the corners of a square of side $2L$. The electric potential at point $P$,which is midway between the two positive charges,is:

At the centre of a half ring of radius $R=10 \ cm$ and linear charge density $\lambda = 4 \ nC \ m^{-1}$,the potential is $x \pi \ V$. The value of $x$ is . . . . .

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 $x=a+r$ (if $a << r$) is: ($\varepsilon_0$ is the permittivity of free space)

$A$ hollow metal sphere of radius $10 \ cm$ is charged such that the potential on its surface becomes $80 \ V$. The potential at the centre of the sphere is . . . . . . . (in $V$)

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 ........ $V$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module