Basic Properties of Electric Charge

Point charge

If the size of a charged body is very small compared with the distances involved, the body is treated as a point charge, with all its charge concentrated at one point in space. Coulomb's law and the point-charge field formula are stated for such charges.

The three basic properties

Charge has three basic properties: additivity, conservation and quantisation. A 3-mark question asking you to state and explain them expects one clean statement plus one illustration each.

Additivity of charge

• The total charge of a system containing $q_1, q_2, \ldots, q_n$ is the algebraic sum $q_1+q_2+\cdots+q_n$, signs included.
• Charge has magnitude but no direction: charges add like real numbers, so charge is a scalar, like mass.
• The one difference from mass: mass is always positive, whereas charge may be positive or negative, so signs must be carried through.
• Worked illustration from NCERT: a system of five charges $+1, +2, -3, +4, -5$ in arbitrary units has total charge $(+1)+(+2)+(-3)+(+4)+(-5) = -1$ in the same unit.

Conservation of charge

• The total charge of an isolated system remains unchanged with time. Charges may be redistributed among the bodies of the system by their interactions, but the algebraic total is constant.
• When two bodies are rubbed, what one gains the other loses — no charge is created or destroyed, only transferred.
• Charged particles themselves may be created or destroyed, but only in equal and opposite pairs. A neutron turning into a proton and an electron creates charges $+e$ and $-e$; the total is zero before and after.
• Conservation has been established experimentally.

Quantisation of charge

• All free charges are integral multiples of a basic unit $e$: $q = ne$, with $n$ any integer, positive, negative or zero.
• $e$ is the magnitude of the charge on an electron or a proton. By convention the electron carries $-e$, the proton $+e$.
• $e = 1.602192\times10^{-19}\,\text{C}$, taken as $1.6\times10^{-19}\,\text{C}$ in numericals.
• Why it must hold: if a body contains $n_1$ electrons and $n_2$ protons, its charge is $n_2e+n_1(-e) = (n_2-n_1)e$, and the difference of two integers is an integer.
• Quantisation was first suggested by Faraday's experimental laws of electrolysis and was demonstrated experimentally by Millikan in 1912.
• When quantisation may be ignored: at the macroscopic level a charge of $1\,\mu\text{C}$ is about $10^{13}$ electronic charges, so the step size $e$ is invisible and charge appears continuous — like a dotted line seen from far away. At the microscopic level, where charges are only tens or hundreds of $e$, they appear in discrete lumps and quantisation cannot be ignored.

Units of charge

• The SI unit is the coulomb (C), defined through the ampere: one coulomb is the charge flowing through a wire in $1\,\text{s}$ when the current is $1\,\text{A}$.
• About $6\times10^{18}$ electrons carry a charge of $-1\,\text{C}$, so the coulomb is a very large unit for electrostatics; the practical units are $1\,\mu\text{C} = 10^{-6}\,\text{C}$ and $1\,\text{mC} = 10^{-3}\,\text{C}$.
• NCERT's estimate: if $10^{9}$ electrons leave a body every second, accumulating $1\,\text{C}$ on another body takes about $200$ years.

How CBSE examines this section

• Charge transferred when a body gains $n$ electrons is $-ne$. A body carrying $+1\,\text{C}$ which gains $5\times10^{18}$ electrons picks up $-5\times10^{18}\times1.6\times10^{-19} = -0.8\,\text{C}$, so its net charge becomes $1-0.8 = +0.2\,\text{C}$.
• Spheres touched together and separated: test the offered answers twice over. First, the algebraic sum of the final charges must equal the algebraic sum of the initial charges (conservation). Second, every final charge must be an integral multiple of $e$ (quantisation) — an option offering $+3.5e$ or $+5.5e$ is ruled out even when its total is right.
• For $+3e$, $+5e$ and $-3e$ brought into simultaneous contact, the total is $+5e$, so only sets summing to $5e$ with integral multiples of $e$, such as $+6e, +6e, -7e$, are possible.