Lessons 3–4 · 2 lessons · P.Q. Habibullayev, A. Boydedayev, A.D. Bahromov, J.E. Usarov, K.T. Suyarov, M.K. Yuldasheva. Physics, textbook for Grade 8 of general secondary schools, revised and enlarged 3rd edition. “O‘qituvchi” Publishing and Printing Creative House, Tashkent, 2019
3
Interaction of charges. Coulomb’s law
Textbook: pp. 12–14
GoalKnow Coulomb’s law (F = k·|q₁|·|q₂|/r²) and the physical meaning of k; calculate the Coulomb force.
New words
point charge · nuqtaviy zaryadCoulomb force · Kulon kuchitorsion balance · buralma tarozik = 9·10⁹ N·m²/C² · k = 9·10⁹ N·m²/C²
Explanation
Charged bodies interact even without touching. In 1785 the French scientist Charles Coulomb measured this force with a torsion balance. His experiments showed that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. A charged body whose size and shape can be ignored is called a point charge. For two stationary point charges in a vacuum, F = k·|q₁|·|q₂|/r², where k = 9·10⁹ N·m²/C²: two charges of 1 C each, 1 m apart in a vacuum, act on each other with a force of 9·10⁹ N. The formula uses the magnitudes of the charges, while the signs give the direction: like charges repel, unlike charges attract. By Newton’s third law the two forces are equal in size and opposite in direction. Before calculating, convert distances to metres and charges to coulombs.
Worked examples
q₁ = 2 nC, q₂ = 5 nC, r = 3 cm = 0.03 m: F = 9·10⁹ · 2·10⁻⁹ · 5·10⁻⁹ : 0.03² = 9·10⁻⁸ : 9·10⁻⁴ = 10⁻⁴ N (0.1 mN).
The same charges at 6 cm: the distance doubled, so the force becomes 2² = 4 times smaller: F = 10⁻⁴ : 4 = 2.5·10⁻⁵ N.
Class activity
“Distance and force”: make a table on paper: with charges fixed and distance 1, 2, 3, 4 units, by what factor does the force fall? Fill it in and state the pattern (1, 1/4, 1/9, 1/16). Only pencil and paper are needed.
Practice
1
State Coulomb’s law in your own words.
The force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance.
2
Charges of 5 µC and 2 µC are 10 cm apart in a vacuum. What is the force in newtons?
9
3
If both charges and the distance are all doubled, how does the force change?
It does not change: the product grows 4 times and the square of the distance also grows 4 times.
4
Why does the formula use the magnitudes of the charges, with the direction found separately?
The formula gives the size of the force; the direction depends on the signs: like charges repel, unlike attract.