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CraftExam
medium difficulty10 min

Electric Charge, Quantisation and Conservation

Electric charge is a fundamental property of matter due to which bodies exert electric forces on one another. It exists in two types, positive and negative, and any observable charge is an integral multiple of the elementary charge: q = ne.

In one line: Gain electrons gives negative charge; loss of electrons gives positive charge. The number part comes from n times e.

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Understand it

  • A body becomes charged when it has an excess or deficiency of electrons.
  • The SI unit of charge is coulomb (C).
  • Charge is additive, so the total charge of a system is the algebraic sum of individual charges.
  • Charge is conserved, meaning total charge in an isolated system remains constant.
  • Charge is quantised because it occurs as q = ne, where n is an integer and e = 1.6 × 10−19 C.
  • At macroscopic scale, the discrete nature is usually not noticed because e is very small.

Example

If a body has 5 × 1012 extra electrons, its charge is q = -ne = -(5 × 1012)(1.6 × 10−19 C) = -8.0 × 10−7 C. The negative sign shows excess electrons.

Formula and rule

Key rules: q = ne, where q is charge in coulomb, n is an integer, and e = 1.6 × 10−19 C.

Total charge is conserved in an isolated system and charges add algebraically.

Use negative sign for excess electrons and positive sign for electron deficiency.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A metal sphere loses 2 × 1010 electrons.

  1. 1Charge developed = ne = (2 × 1010)(1.6 × 10−19 C) = 3.2 × 10−9 C.
  2. 2Since electrons are lost, the sphere becomes positively charged.
  3. 3Final answer: +3.2 × 10−9 C.

Method you can reuse

  1. 1Identify whether electrons are gained or lost.
  2. 2Write q = ne.
  3. 3Substitute n and e with units.
  4. 4Decide the sign from electron gain or loss.
  5. 5State the physical meaning of the sign.

Visual tip

A simple diagram may show a neutral body, electron transfer, and final positive and negative bodies. Useful labels are electrons transferred, body losing electrons, body gaining electrons, and sign of charge.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

Why can the charge on a body be 3.2 × 10−19 C but not 2.4 × 10−19 C?

Think first, then show answer
Charge must be an integral multiple of e = 1.6 × 10−19 C. Since 3.2 × 10−19 C equals 2e, it is possible, but 2.4 × 10−19 C equals 1.5e, which is not allowed because n must be an integer.

Common wrong answer

Writing -3.2 × 10−9 C for a body that loses electrons.

Why it loses marks: Loss of electrons leaves a positive charge.

Don't mix this up

Students often write q = ne but forget that n must be an integer, or they use a positive sign even when the body has excess electrons.

Exam tip

When a question mentions loss of electrons, charge is positive; when it mentions gain of electrons, charge is negative. Always attach the correct sign and SI unit.

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

Usually asked as a short answer on quantisation or conservation, a numerical on number of electrons transferred, or an assertion-reason question about why charge is conserved during charging by friction.
  1. 1

    Enough for 1 mark

    Electric charge is a fundamental property of matter due to which bodies exert electric forces on one another. It exists in two types, positive and negative, and any observable charge is an integral multiple of the elementary charge: q = ne.

  2. 2

    Add for 2 marks

    Example: If a body has 5 × 1012 extra electrons, its charge is q = -ne = -(5 × 1012)(1.6 × 10−19 C) = -8.0 × 10−7 C. The negative sign shows excess electrons.

  3. 3

    Add for 3 marks

    A body becomes charged when it has an excess or deficiency of electrons.

Practice

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