An infinite number of charge, each of charge $1\, \mu C$ are placed on the x-axis with coordinates $x=1, 2, 4, 8, ....... \infty.$ If a charge of $1\,C$ is kept at the origin, then what is the net force acting on $1\,C$ charge?
The schematic diagram of distribution of charges on x-axis is shown in figure
Total force acting on 1 C charge is given by $F=\frac{1}{4\pi\varepsilon_{0}}\left[\frac{1\times1\times 10^{-6}}{\left(1\right)^{2}}+\frac{1\times 1\times 10^{-6}}{\left(2\right)^{2}}+\frac{1\times 1\times 10^{-6}}{\left(4\right)^{2}}+\frac{1\times 1\times 10^{-6}}{\left(8\right)^{2}}+...\infty\right]$ $=\frac{10^{-6}}{4\pi\varepsilon_{0}}\left[\frac{1}{1}+\frac{1}{4}+\frac{1}{16}+\frac{1}{64}+...\infty\right]$ $=9\times10^{-6}\times10^{9}\left(\frac{1}{1-\frac{1}{4}}\right)$ $=9\times10^{9}\times10^{-6}\times\frac{4}{3}=12000\,N$
It is the property of subatomic particles that experiences a force when put in an electric and magnetic field. It is are of two types: Positive and Negative. It commonly carried by charge carriers protons and electrons.
Properties of Electric Charge
Various properties of charge include the following :-
Additivity of Electric Charge
Conservation of Electric Charge
Quantization of Electric Charge
Types of electric charge
Two kinds of electric charges are there :-
Negative Charge - When an object has a negative charge it means that it has more electrons than protons.
Positive Charge - When an object has a positive charge it means that it has more protons than electrons.
When there is an identical number of positive and negative charges, the negative and positive charges would cancel out each other and the object would become neutral.
