An infinite number of charges, each numerical | vedclass

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

Question

(C) The electric potential $V$ at a point due to a system of charges is given by $V = \sum \frac{1}{4\pi\varepsilon_0} \frac{q_i}{r_i}$.Here, the char

Vedclass · Accepted Answer

$\frac{q}{2\pi \varepsilon_0}$

Vedclass · Answer

(C) The electric potential $V$ at a point due to a system of charges is given by $V = \sum \frac{1}{4\pi\varepsilon_0} \frac{q_i}{r_i}$.Here, the charges are $q$ at distances $r = 1, 2, 4, 8, \dots \, 	ext{m}$.$V = \frac{1}{4\pi\varepsilon_0} \left[ \frac{q}{1} + \frac{q}{2} + \frac{q}{4} + \frac{q}{8} + \dots ight]$$V = \frac{q}{4\pi\varepsilon_0} \left[ 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots ight]$The term in the bracket is a geometric progression with first term $a = 1$ and common ratio $r = 1/2$.The sum of an infinite geometric series is $S = \frac{a}{1-r} = \frac{1}{1 - 1/2} = \frac{1}{1/2} = 2$.Therefore, $V = \frac{q}{4\pi\varepsilon_0} 	imes 2 = \frac{2q}{4\pi\varepsilon_0} = \frac{q}{2\pi\varepsilon_0}$.

An infinite number of charges, each numerically equal to $q$ and of the same sign, are placed along the $x-$axis at $x = 1, 2, 4, 8, \dots \, \text{meters}$. The electric potential at $x = 0$ due to this set of charges is:

Similar Questions

Consider two concentric conducting spheres of radii $R$ and $2R$ respectively. The inner sphere is given a charge $+Q$. The outer sphere is grounded. The potential at $r = \frac{3R}{2}$ is

Draw a graph of $V$ versus $r$ for a uniformly charged spherical shell of radius $R$.

$A$ charge of total amount $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R$ $(R > r)$ such that the surface charge densities on the two spheres are equal. The electric potential at the common centre is

An electric point charge $10^{-3} \mu C$ is placed at the origin $(0, 0)$ of an $X-Y$ coordinate system. Two points $A$ and $B$ are situated at $(\sqrt{2}, \sqrt{2})$ and $(2, 0)$ respectively. The potential difference between the points $A$ and $B$ will be.....$volt$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module