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
4
Problem solving
Textbook: pp. 15–17
GoalSolve problems with Coulomb’s law: find force, charge and distance; charge sharing when identical spheres touch.
New words
identical spheres · bir xil o‘lchamli sharlarconversion to SI · SIga o‘tkazishinverse-square relation · teskari kvadrat bog‘lanishequal sharing of charge · zaryadning teng bo‘linishi
Explanation
In Coulomb-law problems we first convert to SI: 1 cm = 10⁻² m, 1 µC = 10⁻⁶ C, 1 nC = 10⁻⁹ C. Then we solve F = k·|q₁|·|q₂|/r² for the unknown; for two equal charges, for example, q² = F·r²/k. If two identical conducting spheres touch and are separated again, the total charge is shared equally: each gets half of the algebraic sum of the charges. When asked how the force changes, it is easiest to write a ratio: if the distance grows n times, the force falls n² times. The answer states the size of the force and, if asked, whether it is attraction or repulsion.
Worked examples
Two spheres with equal charges 30 cm apart repel with 0.9 N. q² = F·r²/k = 0.9 · 0.3² : 9·10⁹ = 9·10⁻¹² C², so q = 3·10⁻⁶ C = 3 µC.
Identical spheres carry +6 µC and –2 µC. After touching and separating, each gets (6 – 2) : 2 = +2 µC. Before, the force was proportional to the product 12, afterwards to 4: the force became 3 times smaller and attraction turned into repulsion.
Class activity
Write a “problem-solving plan” in your notebook: 1) givens and conversion to SI; 2) formula; 3) rearranging; 4) calculation; 5) answer with unit. Then re-solve one example from lesson 3 following this plan.
Practice
1
Two charges 4 cm apart repel with 18 N. At what distance in cm is the force 2 N?
12
2
An identical +8 µC sphere and an uncharged sphere are touched and separated. What is each sphere’s charge in µC?
4
3
Two spheres with equal charges 20 cm apart act on each other with 0.9 N. Find each charge.