A proton (charge +e) and an electron (charge −e) are separated by distance r. The electron exerts a force F on the proton, directed toward the electron. What force does the proton exert on the electron?
AA force greater than F, because the proton is more massive
BA force equal to F directed toward the proton — equal in magnitude but opposite in direction
CNo force, because the electron is negatively charged and cannot exert force on positive charge
DA force F/2, because the force is shared equally between the two charges
Coulomb's law obeys Newton's third law: the force the proton exerts on the electron is equal in magnitude and opposite in direction to the force the electron exerts on the proton. The mass difference is irrelevant — Newton's third law applies regardless of how different the two objects are. Both particles experience the same force magnitude F; they simply accelerate differently due to their mass difference (a = F/m).
Question 2 Multiple Choice
Three positive charges are placed at the corners of a triangle. How would you correctly find the total electrostatic force on one of the charges?
AApply Coulomb's law only to the nearest charge, since distant charges have negligible effect
BAdd the magnitudes of the forces from each of the other two charges
CCalculate the Coulomb force from each other charge separately, then add those forces as vectors
DUse an average distance to compute a single combined force from the other two charges
The principle of superposition states that the total electrostatic force on a charge is the vector sum of the individual Coulomb forces from every other charge. You must compute each pairwise force as a vector (with both magnitude and direction), then add the vectors. Simply adding magnitudes ignores direction and produces the wrong answer whenever forces are not collinear. Superposition is the key tool that makes multi-charge problems tractable.
Question 3 True / False
Electric charge is a type of force — it is what causes the electrostatic force between objects.
TTrue
FFalse
Answer: False
Charge is a property of matter, not a force. Confusing charge with force conflates the cause with the effect. Charge is an intrinsic attribute (like mass) that objects possess; the electrostatic force is what arises between two charged objects because of their charges. An object can have charge without experiencing any force (if no other charges are nearby). The distinction matters: charge is a scalar property measured in coulombs; force is a vector interaction measured in newtons.
Question 4 True / False
If the distance between two point charges is halved, the electrostatic force between them increases to four times its original value.
TTrue
FFalse
Answer: True
True. Coulomb's law states F = kq₁q₂/r². If r is halved (r → r/2), then r² → r²/4, making F → 4kq₁q₂/r² = 4F. This inverse-square relationship is the same mathematical structure as Newton's law of gravitation. Halving the distance quadruples the force; doubling the distance reduces it to one-quarter. This rapid scaling with distance is why electrostatic forces are strong at atomic scales but negligible at large distances for neutral bulk matter.
Question 5 Short Answer
How is Coulomb's law analogous to Newton's law of gravitation, and what is the key difference that makes electrostatics more complex?
Think about your answer, then reveal below.
Model answer: Both laws have the same mathematical form — a force proportional to the product of two source quantities (charges or masses) and inversely proportional to the square of the separation distance: F = kq₁q₂/r² versus F = Gm₁m₂/r². The key difference is that electric charge comes in two signs (positive and negative), while mass has only one sign. This means the electrostatic force can either attract (unlike charges) or repel (like charges), whereas gravity always attracts. The signed nature of q₁q₂ determines the direction of the force, adding complexity absent in gravitation.
The analogy is deep — both are inverse-square laws with superposition — but the signed nature of charge fundamentally changes the physics. It enables shielding, bound atomic states, and the near-neutrality of bulk matter. It also means the net force on a charge in a complex charge distribution requires careful vector addition, since forces from opposite-sign charges point in opposite directions.