Two point charges are separated by a distance of 1 cm. The distance is then increased to 3 cm. By what factor does the electrostatic force change?
ADecreases by a factor of 3
BDecreases by a factor of 9
CIncreases by a factor of 9
DDecreases by a factor of 6
Coulomb's law states F = k|q₁q₂|/r². Tripling the distance (r → 3r) replaces r² with (3r)² = 9r², so the force becomes F/9 — it decreases by a factor of 9. This is the inverse-square law: force falls as the square of the distance, not linearly. A common error is applying a linear factor of 3 rather than 3² = 9. The same inverse-square relationship governs gravity, and for the same geometric reason.
Question 2 Multiple Choice
A negative charge −q is placed exactly halfway between two identical positive charges +q. What is the net electrostatic force on the negative charge?
ADirected toward the left positive charge
BDirected toward the right positive charge
CZero, because the equal attractive forces from each side cancel
DNonzero, directed away from both charges — unlike charges repel at the midpoint
By symmetry, each positive charge exerts an attractive force on −q of equal magnitude, but in opposite directions (one pulls left, the other pulls right). These forces cancel exactly, giving a net force of zero. This result requires careful application of the vector nature of Coulomb's law — you must compute direction as well as magnitude for each force and then add them as vectors. Option D is wrong because unlike charges always attract, not repel. The midpoint is a position of equilibrium (though unstable for transverse displacements).
Question 3 True / False
Doubling the distance between two point charges reduces the electrostatic force between them by half.
TTrue
FFalse
Answer: False
The electrostatic force follows an inverse-square law: F ∝ 1/r². Doubling the distance means r → 2r, so r² → 4r², and F → F/4 — the force is reduced to one-quarter, not one-half. A linear (inverse-first-power) law would reduce force by half when distance doubles. The 1/r² dependence is fundamental and comes from the three-dimensional geometry of how influence spreads from a point source.
Question 4 True / False
Unlike the gravitational force between masses, the electrostatic force between two charges can be repulsive rather than attractive.
TTrue
FFalse
Answer: True
Gravity is always attractive — there is no negative mass. Electrostatic force depends on the signs of the charges: like signs (both positive or both negative) repel, opposite signs attract. This sign dependence is physically profound: it allows macroscopic matter to be electrically neutral (electrons and protons attract and bind), whereas if all matter attracted all other matter electrostatically (like gravity), neutral objects would not exist. The ability to have repulsion is what gives electricity its richness compared to gravity.
Question 5 Short Answer
Why does the electrostatic force between point charges follow an inverse-square law? Explain the geometric reasoning rather than just citing the formula.
Think about your answer, then reveal below.
Model answer: A point charge exerts influence uniformly in all directions. Think of this influence as spreading outward like light from a candle. At distance r, this influence is spread over the surface area of a sphere, which is 4πr². Since the total influence is constant and the surface area grows as r², the intensity per unit area — and thus the force experienced at distance r — must fall as 1/r² to keep the total flux constant across any surrounding sphere.
This geometric argument is not just a heuristic — it becomes Gauss's law when formalized. Any force that propagates in three-dimensional space from a point source and obeys conservation (no 'leakage') must follow an inverse-square law, because that is the only scaling that keeps total flux constant as the sphere radius varies. Gravity obeys the same law for the same reason. The inverse-square character is a consequence of living in three spatial dimensions, not a separate empirical coincidence for each of these forces.