Let V_1 be the potential at the center of a s | vedclass

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

Question

(A) The electric potential $V$ at the center of a square of side $a$ with charges $q$ at each of the $4$ corners is given by $V = 4 	imes \frac{Kq}{r

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(A) The electric potential $V$ at the center of a square of side $a$ with charges $q$ at each of the $4$ corners is given by $V = 4 	imes \frac{Kq}{r}$,where $r$ is the distance from the center to any corner.For a square of side $a$,the diagonal is $a\sqrt{2}$,so the distance $r$ from the center to a corner is $r = \frac{a\sqrt{2}}{2} = \frac{a}{\sqrt{2}}$.For the first square,$a_1 = 1 \ m$,so $r_1 = \frac{1}{\sqrt{2}} \ m$. The potential is $V_1 = 4 	imes \frac{K 	imes 2}{1/\sqrt{2}} = 8\sqrt{2}K$.For the second square,$a_2 = 2 \ m$,so $r_2 = \frac{2}{\sqrt{2}} = \sqrt{2} \ m$. The potential is $V_2 = 4 	imes \frac{K 	imes 2}{\sqrt{2}} = \frac{8K}{\sqrt{2}} = 4\sqrt{2}K$.Therefore,the ratio is $\frac{V_2}{V_1} = \frac{4\sqrt{2}K}{8\sqrt{2}K} = \frac{1}{2}$.

Let $V_1$ be the potential at the center of a square of side $1 \ m$ when the charges at the $4$ corners are $2 \ C$ each. If the same charges are placed at the corners of a square of side $2 \ m$,then the potential at the center of this square is $V_2$. The value of $\frac{V_2}{V_1}$ is

Similar Questions

Three equal charges are placed at the corners of an equilateral triangle. Which of the graphs below correctly depicts the equally-spaced equipotential surfaces in the plane of the triangle? (All graphs have the same scale.)

$A$ thin spherical shell is charged by some source. The potential difference between the two points $C$ (the center) and $P$ (a point on the surface) as shown in the figure is: (Take $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ SI units}$)

$A$ point charge $q$ is surrounded by eight identical charges,each of magnitude $q$,at a distance $r$ as shown in the figure. How much work is done by the forces of electrostatic repulsion when the point charge at the center is moved to infinity?

Eight small drops,each of radius $r$ and having same charge $q$,are combined to form a big drop. The ratio between the potentials of the bigger drop and the smaller drop is

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 $P$ midway between the two positive charges is

Vedclass Test Series

Exam Paper Generator

Online Exam Module