An infinite number of charges,each equal to 0 | vedclass

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

Question

(C) The electric potential $V$ due to a point charge $q$ at a distance $r$ is given by $V = \frac{kq}{r}$.For an infinite number of charges,the total

Vedclass · Accepted Answer

$3.60$

Vedclass · Answer

(C) The electric potential $V$ due to a point charge $q$ at a distance $r$ is given by $V = \frac{kq}{r}$.For an infinite number of charges,the total potential is the sum of individual potentials:$V = \sum \frac{kq}{r} = kq \left( \frac{1}{1} + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots ight)$.Here,$k = 9 	imes 10^9 \, N\cdot m^2/C^2$ and $q = 0.2 	imes 10^{-6} \, C$.The term in the bracket is a geometric progression with first term $a = 1$ and common ratio $r = 1/2$. The sum is $S = \frac{a}{1-r} = \frac{1}{1 - 1/2} = 2$.Substituting the values:$V = (9 	imes 10^9) 	imes (0.2 	imes 10^{-6}) 	imes 2 = 1.8 	imes 10^3 	imes 2 = 3600 \, V$.Since $1000 \, V = 1 \, kV$,the potential is $3.60 \, kV$.

An infinite number of charges,each equal to $0.2\,\mu C$,are arranged in a line at distances $1\,m, 2\,m, 4\,m, 8\,m, \dots$ from a fixed point. The potential at the fixed point is $......\,kV$.

Similar Questions

Electron volt is a unit of

For a conducting sphere of radius $R$ carrying a charge $Q$,what is the electric potential at a distance $x$ from the center inside the sphere?

When a charge of $0.01 \ C$ is moved from point $A$ to point $B$ against an electric field,the work done is $15 \ J$. The potential difference $(V_B - V_A)$ is ....... $V$.

On moving a charge of $20 \; C$ by $2 \; cm$,$2 \; J$ of work is done. The potential difference between the points is (in $V$):

$A$ charge $Q$ is placed at each corner of a cube of side $r$. The potential at the centre of the cube is ($\epsilon_0$ = permittivity of free space).

Vedclass Test Series

Exam Paper Generator

Online Exam Module