Basic Properties of Electric Charge

• Electric charges are considered very small, called point charges, to better understand their properties.
• If the sizes of charged bodies are very small compared to the distances between them, all the charge is assumed to be concentrated at one point in space.

• Electric charges are scalar quantities — they have magnitude and sign but no direction.
• If a system has n charges, the total charge is the algebraic sum of all individual charges: Q = q₁ + q₂ + q₃ + ... + q_n
• Charges add up like real numbers — positive and negative signs must always be included while adding.
• Unlike mass (which is always positive), charge can be positive or negative.
• For example, five charges +1, +2, −3, +4, −5 give a total of: (+1) + (+2) + (−3) + (+4) + (−5) = −1 unit.

• Charges are neither created nor destroyed — they can only be transferred from one body to another.
• When two bodies are rubbed together, what one body gains in charge, the other body loses — no new charge is produced.
• In an isolated system, even if charges get redistributed among many bodies, the total charge always remains the same.
• Nature can create charged particles — for example, a neutron turns into a proton and an electron. The proton carries +e and the electron carries −e, so the total charge remains zero, just as it was before.

• All free charges are always an integer multiple of a basic unit of charge e: q = ne
  where n is any integer (positive or negative).
• The charge on an electron is −e and on a proton is +e.
• The value of the elementary charge is e = 1.602192 × 10⁻¹⁹ C.
• Quantisation of charge was first suggested by Faraday through electrolysis laws and experimentally demonstrated by Millikan in 1912.
• If a body has n₁ electrons and n₂ protons, its total charge is (n₂ − n₁) ⋅ e, always an integer multiple of e.
• At the macroscopic level, the step size e is so tiny that the charge appears continuous, like how a dotted line looks solid from a distance.
• At the microscopic level, charges are only a few multiples of e, so the discrete nature of charge cannot be ignored.

Question: If 10⁹ electrons move out of a body every second, how long does it take to collect a total charge of 1 C?

Think of it this way: Imagine you are filling a large water tank, but your tap releases only a tiny drop every second. It will take a very, very long time to fill the tank. Similarly, each electron carries an incredibly tiny charge, so even 10⁹ (one billion) electrons leaving every second adds up to very little charge per second.

• Charge leaving per second
  = 10⁹ × 1.6 × 10⁻¹⁹ C
  = 1.6 × 10⁻¹⁰ C/s

• Time to collect 1 C = \[\frac {1}{1.6×10^{−10}}\]​ = 6.25 × 10⁹ seconds = approximately 198 years

Conclusion: 1 Coulomb is an enormous amount of charge. Even with a billion electrons leaving every second, it would take about 200 years to gather just 1 C — this is why we use smaller units like μC in electrostatics.

Question: How many positive and negative charges are there in a cup of water (250 g)?

Think of it this way: Every water molecule (H₂O) contains 2 hydrogen atoms and 1 oxygen atom — that gives 10 protons and 10 electrons per molecule. Both charges are equal and opposite, so they cancel out, and water is neutral. But if you count all those charges separately, the numbers are surprisingly huge.

• Number of water molecules in 250 g = \[\frac {250}{18}\] × 6.02 × 10²³

• Each molecule has 10 protons (+) and 10 electrons (−)

• Total positive charge = Total negative charge = \[\frac {250}{18}\] × 6.02 × 10²³ × 10 × 1.6 × 10⁻¹⁹ ≈ 1.34 × 10⁷ C

Conclusion: A single cup of water contains about 13 million Coulombs of both positive and negative charge — they perfectly cancel each other, leaving the water electrically neutral. This shows that enormous charges exist in ordinary matter, completely balanced.