Coulomb's Law (force between multiple charges)

Correct answer: B. Repulsive force

Explanation: Coulomb’s law states that the electric force between two point charges is proportional to q1q2 and acts along the line joining them. Since both charges are positive, q1q2 is positive and the interaction is repulsive: each charge pushes the other away. Option A applies to opposite signs, option D is false for nonzero charges, and gravity may also exist but is not the electric force being asked about.

Correct answer: B. Attractive force

Explanation: Under Coulomb’s law, the sign of q1q2 determines whether the electric interaction attracts or repels. A positive charge multiplied by a negative charge gives a negative product, indicating attraction along the line joining the charges. Thus the charges move toward one another if free to move. Option A reverses the sign rule, C would require zero charge or infinite separation, and D ignores the stated electric interaction.

Correct answer: B. The product of the charges

Explanation: Coulomb’s law gives the magnitude F = k|q1q2|/r². Therefore, with separation r fixed, the force is directly proportional to the product of the magnitudes of the two charges. If either charge increases, the force changes proportionally; the sign determines attraction or repulsion. Option A describes distance, which enters inversely as r², while mass and time do not occur in this electrostatic law.

Correct answer: C. One fourth

Explanation: For fixed charges, Coulomb’s law is F = k|q1q2|/r², so force varies inversely as the square of separation. If the original distance is r and it becomes 2r, then F' = k|q1q2|/(2r)² = F/4. Hence the new force is one-fourth of the original. Doubling or halving would apply to a first-power relation, not this inverse-square law.

Correct answer: B. Four times

Explanation: For unchanged charges, Coulomb’s inverse-square law is F = k|q1q2|/r². Replacing r by r/2 gives F' = k|q1q2|/(r/2)² = k|q1q2|/(r²/4) = 4F. Therefore the force becomes four times its original magnitude. Option A would follow an inverse-first-power law, whereas C and D describe decreases even though reducing separation increases the force.

Correct answer: A. Double

Explanation: Coulomb’s law is F = k|q1q2|/r². When r and the other charge remain fixed, F is directly proportional to the selected charge. Replacing q1 by 2q1 gives F' = k|2q1q2|/r² = 2F, so the force doubles in magnitude. Option B would require both charges to double, while C and D contradict direct proportionality. The interaction’s attractive or repulsive nature is unchanged if the charge’s sign is not reversed.

Correct answer: B. Four times

Explanation: Using Coulomb’s law F = k|q1q2|/r², keep r fixed and replace q1 with 2q1 and q2 with 2q2. The new force is F' = k|(2q1)(2q2)|/r² = 4F. Thus the magnitude becomes four times the original. Option A accounts for only one doubled charge; C and D fail to reflect the fourfold increase in the charge product.

Correct answer: A. Superposition principle

Explanation: The electrostatic superposition principle states that the net force on a charge equals the vector sum of the individual Coulomb forces exerted by every other charge: F_net = F1 + F2 + F3 + … . Each contribution is calculated separately with its magnitude and direction, then combined component-wise or geometrically. Energy conservation is useful in other analyses, but it does not replace this force-summation rule; inertia and pressure are unrelated here.

Correct answer: B. Zero

Explanation: The governing concept is vector addition of forces. Force has both magnitude and direction, so equal magnitudes cannot simply be treated as positive numbers. Taking one force as +F and the opposite force as −F gives F_net = F − F = 0. Thus the two forces cancel completely, making option B correct. Doubling would apply only to equal forces in the same direction; half and four times have no basis here.

Correct answer: A. By adding both forces

Explanation: The governing concept is addition of collinear vectors in the same direction. If the two forces have magnitudes F1 and F2 and point along the same line and direction, their resultant magnitude is F_net = F1 + F2. Therefore option A is correct. Subtraction is used when forces act in opposite directions, while the other choices incorrectly ignore one or both forces.

Correct answer: C. Zero

Explanation: Coulomb's law gives the force between each pair, and superposition requires adding the two force vectors. Each outer positive charge repels the positive middle charge. Because the outer charges are equal and equally distant, both repulsive forces have equal magnitude: one points left and the other right. They cancel, so the net force is zero and option C is correct.

Correct answer: A. Both forces toward left

Explanation: Use the attraction and repulsion rules together with Coulomb's law. The negative charge on the left attracts the middle positive charge toward the left. The positive charge on the right repels the middle positive charge away from the right charge, also toward the left. Hence both individual forces point left, so option A is correct. Equal distance does not cause cancellation because the directions are the same.

Correct answer: B. Vector quantity

Explanation: Coulomb force is a force, and force is fundamentally a vector quantity. Its complete description requires both magnitude, calculated from Coulomb's law, F = k|q1q2|/r², and direction, determined by attraction or repulsion along the line joining the charges. Therefore option B is correct. A scalar has magnitude only, while option C is incomplete and option D omits the magnitude.

Correct answer: B. Force decreases

Explanation: Coulomb's law is F = k|q1q2|/r², so with fixed charges the force is inversely proportional to the square of separation r. Increasing r makes the denominator larger and therefore reduces F. For example, doubling the distance makes the force one-fourth. Thus option B is correct. The force does not remain constant or automatically become zero; its value decreases according to the inverse-square relation.

Correct answer: B. Force increases

Explanation: Coulomb's law states F = k|q1q2|/r². If the distance and medium remain unchanged, the force is directly proportional to the product of the charge magnitudes, |q1q2|. Increasing either charge increases this product and therefore increases the force magnitude. Hence option B is correct. The direction still depends on whether the charges attract or repel; it does not disappear, and the force does not become zero.

Correct answer: D. One ninth

Explanation: For fixed charges, Coulomb's law gives F = kq1q2/r², so force varies inversely as the square of distance. Let the original distance be r and force be F. When the distance becomes 3r, the new force is F' = kq1q2/(3r)² = F/9. Therefore the force becomes one-ninth of its original value, making option D correct; it is not merely one-third.

Correct answer: B. Nine times

Explanation: Coulomb's law gives F ∝ 1/r² when the charges are unchanged. If the original distance is r and the new distance is r/3, then F' / F = r²/(r/3)² = r²/(r²/9) = 9. Thus the new force is nine times the original force, so option B is correct. Choosing three times incorrectly treats the relation as inverse to r rather than inverse to r².

Correct answer: A. Three times

Explanation: Coulomb's law is F = k|q1q2|/r². If the separation, medium, and second charge remain unchanged, replacing q1 by 3q1 changes the force to F' = k|(3q1)q2|/r² = 3F. Therefore the force becomes three times its original magnitude, so option A is correct. Nine times would require both charge magnitudes to triple, while the other choices contradict direct proportionality to charge.

Correct answer: C. Nine times

Explanation: Coulomb’s law states that the magnitude of force is F = k|q₁q₂|/r². If q₁ becomes 3q₁ and q₂ becomes 3q₂, their product becomes (3q₁)(3q₂) = 9q₁q₂. Since the distance r is unchanged, the denominator does not change. Therefore the new force is 9F, so option C is correct; three or six times would account for only part of the change.

Correct answer: B. Half

Explanation: Coulomb’s law gives F = k|q₁q₂|/r². Doubling one charge multiplies the numerator by 2. Doubling the separation changes r² to (2r)² = 4r², so the distance effect divides the force by 4. Combining both independent changes gives F′/F = 2/4 = 1/2. Hence the force becomes half, making option B correct; option D ignores the charge increase.

Correct answer: A. Remain the same

Explanation: For two point charges, F = k|q₁q₂|/r². Doubling both charges changes the charge product by 2 × 2 = 4. Doubling the distance changes the squared distance by 2² = 4, which reduces the force by the same factor. Thus F′/F = 4/4 = 1. The magnitudes and direction therefore remain unchanged, so option A is correct; the other choices retain only one of the two effects.

Correct answer: B. Toward the right

Explanation: Like charges repel according to the electrostatic interaction rule. The source charge is positive and the middle charge is also positive, so the left-hand charge pushes the middle charge away from its position. Away from a charge on the left is toward the right. Therefore option B is correct. The force is not leftward, because that would represent attraction, and it is not zero unless another force exactly cancels it.

Correct answer: A. Toward the left

Explanation: Unlike charges attract each other. A negative charge placed on the left attracts the positive middle charge toward itself. Since the attracting source lies to the left, the force on the middle charge points leftward. Thus option A is correct. A rightward force would correspond to repulsion, which occurs for like charges; the force is not zero because no cancelling force is specified.

Correct answer: A. Toward the left

Explanation: Two positive charges have the same sign, so they repel. The positive charge on the right pushes the middle positive charge away from itself. Moving away from the right-hand source means moving toward the left. Therefore option A is correct. The rightward choice would incorrectly describe attraction, and zero force cannot be concluded because no equal opposing force is given.

Correct answer: B. Toward the right

Explanation: A positive charge and a negative charge are unlike charges, so they attract. The negative source is on the right, and the positive middle charge is pulled toward that source. Consequently, the force points to the right and option B is correct. A leftward force would imply repulsion or a source on the opposite side. The force is not zero because no other force is stated to cancel the attraction.