Coulomb's Law (force between multiple charges)

Correct answer: A. 3 N toward the left

Explanation: Forces along one straight line are treated as signed vectors. Choose right as positive: the 5 N leftward force is −5 N and the 2 N rightward force is +2 N. Their sum is −5 + 2 = −3 N. The negative sign means the resultant points left, with magnitude 3 N. Therefore option A is correct; adding 7 N would ignore the opposite directions.

Correct answer: B. 10 N toward the right

Explanation: Force is a vector, but vectors pointing in the same direction add directly. Both given forces point right, so the resultant magnitude is 4 N + 6 N = 10 N, and its direction remains rightward. Hence option B is correct. Subtracting them would be appropriate only for opposite directions, while a leftward or zero result contradicts the stated common direction and nonzero magnitudes.

Correct answer: C. Zero

Explanation: The governing concept is vector addition of forces. Take upward as positive and downward as negative: F_net = +3 N + (−3 N) = 0 N. The equal magnitudes cancel because the directions are opposite, so the charge has no net force. Option A incorrectly adds magnitudes without considering direction, while B and D leave an unbalanced force. Therefore, option C is correct.

Correct answer: A. Along the line joining the two charges

Explanation: Coulomb’s law describes a central force, meaning the force acts along the straight line joining the centres of the two charges. Like charges repel along this line, whereas unlike charges attract along the same line. The actual direction depends on the signs and positions of the charges, not on an absolute upward, circular, or ground-based direction. Hence option A is correct.

Correct answer: B. Newton

Explanation: The governing concept is the SI measurement of force. Coulomb’s law calculates electrostatic force, and every force in the SI system is measured in newtons: F = ma, so its unit is kg·m·s⁻², called the newton (N). Coulomb is the unit of charge, metre is the unit of length, and joule is the unit of energy. Therefore, option B is correct.

Correct answer: B. Coulomb

Explanation: The governing concept is the SI unit of electric charge. Charge is measured in coulombs, represented by C. One coulomb is the amount of charge transported by a current of one ampere in one second, so Q = It gives 1 C = 1 A·s. Newton measures force, metre measures length, and pascal measures pressure. Thus option B is correct.

Correct answer: B. Magnitude remains the same

Explanation: Coulomb’s law gives the magnitude as F = k|q₁q₂|/r². This expression uses the absolute values of the charges, so reversing one or both signs does not change the magnitude when the charge magnitudes and separation remain fixed. The signs do affect whether the interaction is attraction or repulsion. Therefore option B is correct; the other choices confuse direction with magnitude.

Correct answer: A. Because force is a vector quantity

Explanation: Force is a vector quantity because it has both magnitude and direction. For several charges, the net force is the vector sum of the individual Coulomb forces. Forces in the same direction reinforce each other, while opposite components may cancel; perpendicular components must be combined component-wise. Option A states this principle. Option B is false because force is not scalar, and C and D contain incorrect physical claims.

Correct answer: B. By vector addition

Explanation: Perpendicular forces must be treated as vectors because their directions differ. If their magnitudes are F₁ and F₂, the magnitude of the resultant is generally R = √(F₁² + F₂²), and its direction satisfies tan θ = F₂/F₁ when the components are chosen along perpendicular axes. Thus vector addition, not ordinary addition or subtraction, is required. Option B is correct.

Correct answer: B. Smaller

Explanation: Coulomb’s law states that the force magnitude is F = k|q₁q₂|/r². When the charge magnitudes are equal, increasing the separation r reduces the force according to the inverse-square relationship. For example, doubling the distance makes the force one-fourth as large, not zero. Therefore the farther equal charge produces a smaller force, so option B is correct.

Correct answer: A. Nearby charge

Explanation: For two source charges of equal magnitude acting on the same small charge, Coulomb’s law gives F = k|Qq|/r². The only changing factor is the distance r. Because the nearby charge has the smaller separation, its force is larger; the inverse-square relation makes this increase especially strong. The farther charge is weaker, not equal or zero. Hence option A is correct.

Correct answer: B. No, different distances make the forces different

Explanation: Coulomb’s law depends on both charge magnitude and separation: F = k|q₁q₂|/r². Although the two outer charges have equal magnitudes, different distances from the middle charge give different values of r, so the individual force magnitudes are generally unequal. Equality would require equal distances as well. Thus option B is correct; equal charges alone do not ensure equal forces.

Correct answer: C. Both charge and distance

Explanation: Coulomb’s law gives the force magnitude as F = k|q₁q₂|/r². Thus, a larger charge tends to increase the force, while a greater separation decreases it according to the inverse square of distance. Because these effects compete, both charge magnitude and distance must be compared. Option A ignores separation, option B ignores charge, and option D has no physical role.

Correct answer: A. Individual forces may exist but cancel

Explanation: Net force is the vector sum of all forces, not simply a statement that every force is absent. For example, two equal forces of 5 N acting in opposite directions have a resultant of 0 N. Therefore individual electric forces can exist and cancel. Option B confuses zero resultant with zero individual forces; same-direction forces generally add rather than cancel.

Correct answer: B. Both will repel it and the net force will be zero

Explanation: Like charges repel, so each outer negative charge pushes the middle negative charge away from itself. Since the outer charges have equal magnitude and are at equal distances, Coulomb’s law gives equal force magnitudes. These forces point in opposite directions along the same line, so their vector sum is zero. The forces exist; they do not disappear individually.

Correct answer: C. Zero

Explanation: Each positive outer charge attracts the negative middle charge. The left positive charge pulls it leftward, while the right positive charge pulls it rightward. Equal charge magnitudes and equal distances make the two Coulomb forces equal in magnitude. Because they are opposite vectors, they cancel and the resultant force is zero. This conclusion depends on the stated symmetry.

Correct answer: A. The rightward force is larger and the leftward force is smaller

Explanation: When two forces act along one line in opposite directions, the resultant points in the direction of the larger force and has magnitude equal to their difference. Thus, if the rightward force is larger than the leftward force, F_net = F_right − F_left is positive toward the right. Equal forces give zero, while a larger leftward force reverses the direction.

Correct answer: B. The leftward force is larger

Explanation: For two collinear forces pointing in opposite directions, subtract the smaller magnitude from the larger one. The resultant follows the direction of the larger force. Therefore a leftward force greater than the rightward force produces a net force toward the left. Equal forces cancel to zero, whereas a larger rightward force would produce a rightward resultant.

Correct answer: A. In the denominator

Explanation: Coulomb’s law is F = k|q₁q₂|/r², where r is the separation between the charges. The squared distance is in the denominator, so force varies inversely as r². If the distance becomes twice as large, the force becomes one-fourth, provided the charges remain unchanged. It is not part of the force’s direction or merely a unit convention.

Correct answer: B. The pair of larger charges

Explanation: For a fixed separation, Coulomb’s law reduces the comparison to F ∝ |q₁q₂| because k and r² are the same for both pairs. A pair containing larger charge magnitudes has the larger product and therefore the greater force. A zero charge makes the product and force zero. The result assumes that “larger charges” means larger magnitudes, regardless of sign.

Correct answer: B. Zero

Explanation: Coulomb’s law states F = k|q₁q₂|/r². If either q₁ or q₂ is zero, the product q₁q₂ equals zero, so the electrostatic force is zero for any finite separation r. The force cannot be maximum, infinite, or double merely because one charge is absent. Other non-electric forces, if present, are outside this question.

Correct answer: A. Equal

Explanation: By Newton’s third law, the force exerted by charge 1 on charge 2 and the force exerted by charge 2 on charge 1 are equal in magnitude and opposite in direction. Coulomb’s law gives the same magnitude k|q₁q₂|/r² for both interactions. The forces act on different charges, so they do not cancel each other on a single object. Hence option A is correct.

Correct answer: A. Identify the separate force and direction due to each charge

Explanation: The governing concept is the superposition principle: the force on a selected charge is the vector sum of the individual Coulomb forces produced by all other charges. First identify each pairwise force, calculate or compare its magnitude, and mark its direction from attraction or repulsion. Only then add the forces vectorially. Options B, C, and D incorrectly omit real forces or their directions.

Correct answer: A. Ignoring the directions of forces

Explanation: Coulomb force is a vector, so both magnitude and direction are essential. In a multiple-charge problem, the force from one charge may oppose or support the force from another. If directions are ignored and magnitudes are simply added, the net result can be wrong. Converting distance to metres and writing charge units are correct practices, not mistakes; merely counting charges is also not the central error.

Correct answer: B. The force becomes double

Explanation: Coulomb's law gives the magnitude of force as F = k|q1q2|/r². With distance r unchanged, the force is directly proportional to the product q1q2. Replacing one charge by 2q1 changes the product to twice its original value, so the force becomes 2F. The force remains repulsive because both charges are positive. Therefore option B is correct; options A, C, and D do not follow the proportionality.