Basic Properties of Electric Charge വൈദ്യുത ചാർജ്
We know there are two kinds of charge whose effects cancel. Electric charge (വൈദ്യുത ചാർജ്) has three more basic properties, and every numerical in this chapter quietly uses them: charges add like ordinary numbers, the total charge of an isolated system never changes, and charge always comes in whole-number lumps of e. Here you test each one, and find out why one coulomb is a giant unit.
- Powers of ten and prefixes: 1 μC = 10−6 C, 1 nC = 10−9 C, 1 mC = 10−3 C (page 2).
- Rubbing transfers electrons (page 4).
1. Point charges
If the sizes of charged bodies are very small compared with the distances between them, we treat them as point charges (ബിന്ദു ചാർജ്): all the charge of the body is imagined to be concentrated at one point in space. This makes calculations simple, and it is the assumption behind Coulomb's law (page 7).
There is no sharp cut-off; this lab uses "r at least 10 times R" as a rule of thumb. Coulomb's experiments used small spheres far apart for exactly this reason.
2. Additivity of charges (1.5.1)
If a system contains point charges q1, q2, …, qn, its total charge is simply their algebraic sum: q1 + q2 + q3 + … + qn. Charges add up like real numbers – charge is a scalar (അദിശം), like mass: it has magnitude but no direction. This property is the additivity of charge (ചാർജിന്റെ സങ്കലനീയത). One difference from mass: mass is always positive, but charge can be positive or negative, so we must keep the signs when adding.
The starting values are the textbook's example: (+1) + (+2) + (−3) + (+4) + (−5) = −1 (in some arbitrary unit). Try to make the total zero with all five charges non-zero.
3. Charge is conserved (1.5.2)
When two bodies are rubbed, what one body gains in charge, the other loses. Within an isolated system, charges may get redistributed by interactions, but the total charge of the isolated system is always conserved. This is the conservation of charge (ചാർജ് സംരക്ഷണം), established by experiment. It is not possible to create or destroy the net charge of an isolated system – even though charge-carrying particles may be created or destroyed.
Identical conductors share the total charge equally (by symmetry) – Coulomb used exactly this trick to halve charges (page 7). Whatever the values, the total before and after is the same.
4. Quantisation of charge (1.5.3)
Experiments show that all free charges are integral multiples of a basic unit of charge e:
e is the charge of a proton; the electron carries −e (by convention). This is the quantisation of charge (ചാർജിന്റെ ക്വാണ്ടീകരണം). It was first suggested by Faraday's laws of electrolysis and demonstrated experimentally by Millikan in 1912 (oil-drop experiment). If a body contains n1 electrons and n2 protons, its charge is n2e + n1(−e) = (n2 − n1)e – a whole number times e, which can change only in steps of e.
- SI unit of charge: the coulomb (C) – the charge that flows through a wire in 1 s when the current is 1 A.
- e = 1.602192 × 10−19 C; in numericals use e = 1.6 × 10−19 C.
- Number of electrons in −1 C: 1 ÷ (1.6 × 10−19) = 6.25 × 1018 (the textbook says "about 6 × 1018").
- Practical units: 1 μC (microcoulomb) = 10−6 C; 1 mC (millicoulomb) = 10−3 C.
Try 4.8 × 10⁻¹⁹ C (allowed), 2.4 × 10⁻¹⁹ C (impossible – it would be 1.5 e), 1 μC and 1 C. Negative values mean extra electrons.
Why don't we notice the lumps? – the dotted line
The step size e is tiny. At the macroscopic level we deal with charges of a few μC, and 1 μC is about 1013 times e. At that scale, the fact that charge can only change in steps of e is invisible: the grainy nature of charge is lost and it appears continuous – just as a dotted line seen from far away looks like a continuous line. At the microscopic level (a few tens or hundreds of e, which can be counted) quantisation cannot be ignored. It is the scale that matters.
5. Example 1.2 – how long to collect one coulomb?
Q. If 109 electrons move out of a body to another body every second, how much time is required to get a total charge of 1 C on the other body?
First find the charge transferred in one second: (number of electrons per second) × e. Then time = total charge ÷ charge per second. Finally divide the seconds by 365 × 24 × 3600 to get years.
A cube of copper of side 1 cm contains about 2.5 × 1024 electrons. Rubbing moves only a tiny fraction of these.
6. Example 1.3 – charge in a cup of water
Q. How much positive and negative charge is there in a cup of water?
Assume the cup holds 250 g of water. One mole of water (6.02 × 1023 molecules) has a mass of 18 g. Each H2O molecule has 2 + 8 = 10 electrons and 10 protons.
- 🧪 Balloons and Static Electricity (PhET simulation) PhET, University of Colorado Boulder
Rub a balloon on a sweater and watch electrons move; see induction on the wall. - 🧪 John Travoltage (PhET simulation) PhET, University of Colorado Boulder
Rub a foot on a carpet and get a spark from a door knob. - 📄 Static Electricity tutorial The Physics Classroom
Charge, charging methods, induction and electroscopes explained step by step. - 📄 Charging by Induction The Physics Classroom
Animated steps of charging two spheres by induction. - 📄 Triboelectric effect Wikipedia
Why some materials give electrons and others take them when rubbed. - 📄 Electroscope Wikipedia
The gold-leaf electroscope and how it detects charge. - 📄 Oil drop experiment Wikipedia
How Millikan showed that charge is quantised (Exercise 1.25).
7. Check yourself
- Point charge: size negligible compared with the distances involved.
- Additivity: total charge = algebraic sum (charge is a scalar; keep the signs).
- Conservation: the total charge of an isolated system is constant; particles may be created only in pairs of opposite charge (n → p + e).
- Quantisation: q = ne, e = 1.6 × 10−19 C; about 6.25 × 1018 electrons make 1 C; negligible at the macroscopic scale.
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