Charging without physical contact is called : (a) charging by friction (b) charging by conduction (c) charging

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Q. Charging without physical contact is called :

(a) charging by friction

(b) charging by conduction

(d) None of these

Punjab PsebPSEB Punjab Class 12 Board 2023MCQ· 1mImportance★★★★★

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Concept understanding — Quantization of Charge

Quantization of Charge

Imagine you are at a water fountain. You can fill your bottle with any amount of water — a little, a lot, or anything in between. Water is continuous. Now imagine instead that you are buying marbles. You can only buy marbles in whole numbers: 1 marble, 2 marbles, 15 marbles. You cannot buy half a marble or 2.7 marbles. Electric charge behaves like marbles, not like water.

That is the core intuition: charge comes in discrete packets. You cannot have an arbitrary amount of charge. You can only have whole-number multiples of a smallest possible chunk.

The smallest chunk: the elementary charge

That smallest chunk is called the elementary charge, denoted by the symbol $e$ . Its value is:

e = 1.602 \times 10^{-19} \text{ coulombs}

This is the magnitude of charge carried by a single proton (positive) or a single electron (negative). A proton has charge $+e$ , an electron has charge $-e$ .

Important

Every charged object in the universe — from a rubbed balloon to a lightning bolt — carries a total charge that is an integer multiple of $e$ . No exception has ever been observed among free, isolated charges. (Quarks carry fractional charges of $\pm e/3, \pm 2e/3$ but are always confined inside composite particles such as protons and neutrons, whose own net charge is still an integer multiple of $e$ .)

The precise statement

If $q$ is the total charge on any object, then:

q = n e

where $n$ is an integer ( $n = 0, \pm 1, \pm 2, \pm 3, \dots$ ).

The sign of $n$ tells you whether the charge is positive or negative. The magnitude $|n|$ tells you how many elementary charges are present (in excess or deficit).

q = n e, \quad n \in \mathbb{Z}

Why this matters

This is not a mathematical trick. It is a fundamental law of nature. It means:

You cannot have a charge of $0.5e$ or $1.7e$ .
If you measure the charge on any object, you will always find it to be $0$ , $\pm e$ , $\pm 2e$ , $\pm 3e$ , and so on.
All charge transfer — rubbing, conduction, induction — happens by moving whole electrons or protons. You cannot transfer a fraction of an electron.

Watch out

A common mistake is to think that because charge values like $3.2 \times 10^{-19} \text{ C}$ look like decimals, they are not multiples of $e$ . But $3.2 \times 10^{-19} \text{ C}$ is exactly $2e$ (since $2 \times 1.6 \times 10^{-19} = 3.2 \times 10^{-19}$ ). Always check by dividing by $e$ — the result must be an integer.

A concrete example

A glass rod rubbed with silk acquires a charge of $+4.8 \times 10^{-19} \text{ C}$ . How many electrons were transferred?

Divide the total charge by $e$ :

n = \frac{+4.8 \times 10^{-19}}{1.6 \times 10^{-19}} = +3

So the rod lost exactly 3 electrons. It could not have lost 2.5 or 3.7 electrons. The charge is $+3e$ .

Why this is called "quantization" …