Three charges A, B, and C are placed in space. A new charge D is added nearby. How does adding D affect the force between A and B?
AD's electric field partially screens A and B, reducing the force between them
BAdding D increases the total electric field in the region, increasing the force between A and B
CThe force between A and B is unchanged — each pair interacts independently by the superposition principle
DIt depends on whether D has the same or opposite sign as A and B
The superposition principle states that the force between any two charges is completely independent of all other charges. Charge D contributes its own forces on A and on B, but it does not alter the A-B interaction in any way. Superposition means forces add linearly — D's presence doesn't screen, amplify, or modify the pairwise A-B force. This non-obvious independence is what makes electrostatics tractable: you can analyze each pair separately and add the results.
Question 2 Multiple Choice
A positive charge Q is placed at the origin. A positive test charge q is placed to its right. Which of the following correctly describes the force on q?
AA scalar magnitude F = kQq/r² directed toward Q, since opposite charges attract
BA vector of magnitude kQq/r² pointing to the right, away from Q, since like charges repel
CA vector of magnitude kQq/r² pointing to the left, toward Q, since the field pulls inward
DA scalar F = kQq/r² with no direction, since the charges are stationary
Coulomb's law gives a vector force. Like charges (both positive) repel, so the force on q points away from Q — to the right. The magnitude is kQq/r². Option A has the direction wrong (that would be attraction between opposite charges). Option D treats the force as a scalar, which is incorrect — direction is essential for computing net forces when multiple charges are present. Option C would apply to opposite-sign charges.
Question 3 True / False
The superposition principle implies that when computing the net force on a charge due to three others, you must add the three Coulomb forces as vectors, not as scalar magnitudes.
TTrue
FFalse
Answer: True
Force is a vector quantity with both magnitude and direction. Three forces on the same charge generally point in different directions; adding their magnitudes gives the wrong answer except in special symmetric cases. You must decompose each force into x and y (and z) components, sum the components, and reconstruct the resultant vector. This is not optional bookkeeping — it is the only physically correct procedure. The superposition principle says the interactions are independent; vector addition is how you combine them into a net result.
Question 4 True / False
Coulomb's law predicts that doubling the distance between two charges doubles the force between them.
TTrue
FFalse
Answer: False
Coulomb's law is an inverse-square law: F = kq₁q₂/r². Doubling the distance (r → 2r) gives F ∝ 1/(2r)² = 1/(4r²), so the force decreases by a factor of 4, not 2. This 1/r² dependence, the same as gravity, means electrostatic forces fall off rapidly with distance. Confusing inverse-square with inverse-linear is a common error — the exponent on r in the denominator is 2, not 1.
Question 5 Short Answer
Why must Coulomb forces be treated as vectors rather than scalars when finding the net force on a charge from multiple sources?
Think about your answer, then reveal below.
Model answer: Each Coulomb force has a direction determined by the line connecting the two charges involved. When multiple forces act on the same charge from different directions, adding their magnitudes (scalar addition) ignores directionality and gives a physically wrong result. The correct procedure is vector addition: decompose each force into components, sum each component independently, and reconstruct the net force. The geometry of where the source charges are located determines the directions, which can cause forces to partially cancel or reinforce depending on angles.
The point of vector addition is that forces in perpendicular directions don't interfere — a 3 N force eastward and a 4 N force northward produce a 5 N force to the northeast, not a 7 N force in some vague direction. Scalar addition would give 7 N, which is wrong. In electrostatics, charge positions determine force directions, and those directions are almost never aligned — so vector decomposition is always necessary.