10 min readConcept sheetSection A MCQ (1 mark), fill-in-the-blank parts and the passage (5 marks); Section B very short answer (2 marks) on charging by rubbing or how the force changes with distance

Electric charges, Coulomb's law, conductors and insulators

Rubbing moves electrons from one body to another; like charges repel and unlike charges attract. Coulomb's law: F = kq₁q₂/r², so the force falls with the square of distance.

Coulomb's lawF = kq₁q₂/r², with k = 9 × 10⁹ N m² C⁻² in vacuum or air

Charge of an electron1.6 × 10⁻¹⁹ C (negative); 1 C is the charge of 6.25 × 10¹⁸ electrons

Two kinds of chargeGlass rubbed with silk: positive. Ebonite rubbed with fur or wool: negative

SI unit of chargecoulomb (C)

Static electricity and two kinds of charge

Run a plastic comb through dry hair and it picks up bits of paper. The comb has become charged by rubbing. Charge made by rubbing is called frictional or static electricity. Rubbing does not create charge. It only moves electrons from one body to the other. The body that loses electrons becomes positively charged. The body that gains electrons becomes negatively charged, by the same amount. The positive charges (protons) stay fixed inside the atoms. A glass rod rubbed with silk becomes positive. An ebonite rod rubbed with fur or wool becomes negative. Like charges repel each other and unlike charges attract. Benjamin Franklin named the two kinds positive and negative.

Activity: charged straws

You need two plastic straws, a thread, cello tape, a sheet of paper, a small glass bottle and a piece of silk.

1
Tie a thread to the middle of a drinking straw. Hang it from the edge of a table with cello tape so that it hangs level.
2
Bring a second straw near one end of it. Observe: nothing happens, because neither straw is charged.
3
Rub the hanging straw with a piece of paper. Bring the uncharged straw near it. Observe: the hanging straw moves towards it.
4
Now rub the second straw with paper too and bring it near. Observe: the hanging straw is pushed away. Two like charges repel.
5
Rub a small glass bottle with a silk cloth and bring it near the charged straw. Observe: the straw is pulled towards the bottle.
6
Conclude.
The glass and the straws carry different kinds of charge. Like charges repel and unlike charges attract.

Conservation of charge, and why charge leaks away

Conservation of charge: in an isolated system, the total charge stays the same. Charge only moves from one body to another.
Charge is carried by electrons. Each electron has a charge of 1.6 × 10⁻¹⁹ C, so 1 C needs about 6.25 × 10¹⁸ electrons.
If a charged pen is rolled between your palms, it loses its charge. The charge leaks away through your body to the earth.
A metal rod held in the bare hand cannot be charged by rubbing. Charge flows along the metal and through you to the earth.
After walking on a nylon or woollen carpet you may get a small shock from a metal door knob. Charge built up by friction jumps across.

Coulomb's law

The lawThe force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

FormulaF = kq₁q₂/r², where q₁ and q₂ are the charges in coulombs and r is the distance in metres.

The constant k9 × 10⁹ N m² C⁻² for vacuum or air. It depends on the medium.

DirectionAlong the line joining the two charges: repulsion for like charges, attraction for unlike charges.

Distance doubledThe force becomes one quarter, because F ∝ 1/r².

1 coulombTwo charges of 1 C each, 1 m apart in vacuum, repel with a force of 9 × 10⁹ N. Your NIOS lesson prints this force as 9 × 10⁻⁹ N, and then as 1 N: both are misprints. Its answer key gives the correct 9 × 10⁹ N.

Conductors vs insulators

ConductorsLet charge (current) flow through them freely, because they have many free electrons. Examples: silver, copper, aluminium, iron, the human body and the earth.

InsulatorsDo not let charge flow freely, because they have almost no free electrons. Examples: rubber, glass, plastic, bakelite, mica and dry wood.

Insulators can be charged by rubbing because the charge stays where it is made. That is why a plastic comb, not a steel spoon in your hand, picks up paper.

Coulomb's law and counting electrons

Problem

(a) Two charges of +2 μC and +3 μC are 30 cm apart in air. Find the force between them. (b) How many electrons must be removed from a neutral body to give it a charge of +3.2 × 10⁻⁹ C? (k = 9 × 10⁹ N m² C⁻², e = 1.6 × 10⁻¹⁹ C)

Working

(a) Change to SI units: q₁ = 2 × 10⁻⁶ C, q₂ = 3 × 10⁻⁶ C, r = 0.30 m.
F = kq₁q₂/r² = (9 × 10⁹ × 2 × 10⁻⁶ × 3 × 10⁻⁶) ÷ (0.30)².
Top: 9 × 10⁹ × 6 × 10⁻¹² = 5.4 × 10⁻². Bottom: 0.09.
F = 0.054 ÷ 0.09 = 0.6 N. Both charges are positive, so the force is repulsive.
(b) Number of electrons n = q/e = (3.2 × 10⁻⁹ C) ÷ (1.6 × 10⁻¹⁹ C) = 2 × 10¹⁰.

Answer

(a) 0.6 N, repulsive; (b) 2 × 10¹⁰ electrons

In real life

On a dry winter day a synthetic sweater crackles as you pull it off. A metal door handle can give a small shock after you walk on a carpet. Lightning in a monsoon storm is the same static charge on a giant scale.

Exam angle

1 marks: “Name the SI unit of electric charge.” The coulomb (C).

2 marks: “How does the force between two charges change if the distance between them is halved?” F ∝ 1/r². Halving r makes r² one quarter, so the force becomes four times as large.

2 marks: “Why can a metal rod held in the bare hand not be charged by rubbing, while a plastic comb can?” Metal is a conductor: the charge flows along it and through the body to the earth. Plastic is an insulator, so the charge stays on the comb.

Remember it

Lose electrons, go plus; gain electrons, go minus. Coulomb's force: product on top, distance squared below.