Coulomb's Law (force between multiple charges)

Correct answer: B. Toward left

Explanation: Both charges are positive, so their electrostatic interaction is repulsive. The source charge lies to the right of the target, and repulsion pushes the target away from the source. Away from a charge on the right means toward the left. The force is not zero because both charges are nonzero, and no vertical component is specified. Thus the correct direction is leftward, option B.

Correct answer: A. Toward right

Explanation: Coulomb’s law states that charges with the same sign repel one another. The positive charge located on the left pushes the positive target charge away from itself. Away from a source on the left means toward the right. Therefore, option A is correct. The force is not leftward, downward, or zero because the charges are separated and exert repulsive force.

Correct answer: B. Toward right

Explanation: Opposite electric charges attract according to Coulomb’s law. Since the positive charge is positioned on the right of the negative target charge, the target is pulled toward that positive charge. Hence the force on the target is directed to the right, making option B correct. It is not repulsion, leftward, upward, or zero because the charges have opposite signs and are separated.

Correct answer: B. Toward right

Explanation: The governing principle is electrostatic repulsion between charges having the same sign. The negative source charge lies to the left of the negative target charge, so it pushes the target away from the left side. The target therefore experiences a force toward the right, which is option B. The force is not zero because both charges are present and separated by a finite distance.

Correct answer: B. Newton

Explanation: Coulomb’s law describes the electrostatic force between charged particles, and force is measured in the SI unit newton, written as N. Therefore, option B is correct. Coulomb is the SI unit of electric charge, metre measures length, and second measures time. Although charge and distance occur in Coulomb’s law, their units are not the unit of the resulting force.

Correct answer: A. Equal magnitude and opposite direction

Explanation: Newton’s third law applies to the mutual electrostatic forces of two charges. If charge 1 exerts a force on charge 2, charge 2 exerts a force of equal magnitude in the opposite direction on charge 1. The forces may be attractive or repulsive depending on charge signs, but their action–reaction relationship is always equal and opposite. Hence option A is correct.

Correct answer: A. Because the product of the charges is zero

Explanation: Coulomb’s law is F = k|q₁q₂|/r², so the magnitude of electrostatic force is proportional to the product q₁q₂. If either charge is zero, this product is zero and F becomes zero, provided the separation is finite and nonzero. Thus option A is correct. The distance does not need to be zero, equal charges do not imply zero force, and a zero magnitude does not mean direction causes the result.

Correct answer: A. Nature or direction of force

Explanation: In Coulomb’s law, the magnitude of force depends on |q₁q₂| and the separation r, whereas the signs determine whether the interaction is attractive or repulsive. If the signs change while magnitudes and distance remain fixed, the numerical magnitude can remain the same, but the nature and vector direction of the force may reverse. Thus option A is correct.

Correct answer: A. Rightward force

Explanation: For two forces acting along one straight line in opposite directions, the net force equals the difference between their magnitudes and points toward the larger force. Since the resultant is directed to the right, the rightward force must exceed the leftward force. If they were equal, the net force would be zero; if the left force were larger, the result would point left. Hence option A is correct.

Correct answer: B. Leftward force

Explanation: When two collinear forces act in opposite directions, their resultant points toward the force with the greater magnitude. A net force toward the left therefore means that the leftward force is larger than the rightward force. Equal forces would cancel and produce zero net force, while a larger rightward force would give a rightward result. Consequently, option B is correct.

Correct answer: A. Equal

Explanation: Coulomb’s law gives the force magnitude as F = k|qQ|/r². For both source charges, q is equal, the target charge Q is the same, and the distance r is equal. Therefore the numerator and denominator are identical, so both force magnitudes are equal. Their directions could differ because of charge signs or positions, but that does not change the equality of magnitudes. Thus option A is correct; the other choices contradict the stated conditions.

Correct answer: B. The closer one

Explanation: For a fixed target charge and equal source charges, Coulomb’s law reduces to F ∝ 1/r². Hence the force becomes larger as the separation r becomes smaller. The charge that is closer to the target therefore exerts the greater force. The farther charge produces a weaker force, not an equal one, because the inverse-square dependence matters. Option B is correct; the force is not automatically zero or absent.

Correct answer: A. Increase the distance

Explanation: For unchanged charges, Coulomb’s law gives F = k|q₁q₂|/r², so the only listed controllable factor is the separation r. Increasing r makes the denominator larger and reduces the force according to the inverse-square relation. For example, doubling the distance changes the force to F/4. Decreasing distance or increasing either charge would increase the force instead. Therefore option A is the correct method.

Correct answer: B. Decrease the distance

Explanation: Coulomb’s law states F = k|q₁q₂|/r². Since both charges remain fixed, the force can be increased by reducing the separation r. The inverse-square dependence means that if the distance is halved, the force becomes four times larger, assuming the point-charge model remains applicable. Increasing distance would decrease the force, making one charge zero would make it zero, and ignoring distance is not physical. Thus option B is correct.

Correct answer: C. Twice the magnitude of one force

Explanation: Forces are vectors, so forces pointing in the same direction are added rather than cancelled. If each force has magnitude F, then the resultant magnitude is F_net = F + F = 2F, and its direction is the common direction of the two forces. A zero result would occur for equal forces in opposite directions, not the same direction. Therefore option C is correct; options B and D do not represent the required vector sum.

Correct answer: A. Zero

Explanation: Force is a vector, so both magnitude and direction must be considered. For two collinear forces of equal magnitude F acting in opposite directions, their vector sum is F + (−F) = 0. Therefore the net force is zero, making option A correct. The other choices would require unequal magnitudes or forces acting in a non-opposite arrangement.

Correct answer: A. First signs, then distance, then separate forces, then vector sum

Explanation: For several charges, Coulomb’s law must be applied pair by pair: F = k|q₁q₂|/r². First identify charge signs to determine attraction or repulsion, then use each separation to calculate the individual magnitudes. Finally assign directions and add the forces as vectors. Thus option A is correct; direct scalar addition or ignoring direction can produce a wrong result.

Correct answer: A. One newton

Explanation: Coulomb’s law states that, for unchanged charges, electrostatic force varies inversely as the square of separation: F ∝ 1/r². If the distance becomes 4r, the new force is F' = F/4² = 16/16 = 1 N. Therefore option A is correct. Option B would use an inverse-first-power relation, while C and D do not apply the required square dependence.

Correct answer: A. One and a half times

Explanation: At fixed separation, Coulomb’s law shows that the force is proportional to the product q₁q₂. The first charge contributes a factor of 3 and the second contributes a factor of 1/2. Therefore F'/F = 3 × 1/2 = 3/2, or 1.5. The new force is one and a half times the original, making option A correct; B ignores the second change and D multiplies instead of halving.

Correct answer: C. Equal in both

Explanation: For equal separation, Coulomb’s law makes the force proportional to the product of the two charge magnitudes. For the first pair, q₁q₂ = 2 × 6 = 12 C². For the second pair, q₁q₂ = 3 × 4 = 12 C². Since k and r² are also the same, both force magnitudes are equal. Thus option C is correct; comparing individual charges instead of their products would be misleading.

Correct answer: C. Equal in both

Explanation: Coulomb’s law is F = kq₁q₂/r². Both pairs have the same separation, 2 m, so only the charge products need comparison. The first product is 2 × 8 = 16, and the second is 4 × 4 = 16. The common factors k and r² cancel in the comparison, giving equal force magnitudes. Therefore option C is correct; neither pair has zero force because none of the charges is zero.

Correct answer: A. Upward

Explanation: Opposite electric charges attract according to Coulomb’s law. Therefore the negative charge at the centre is pulled toward the positive charge located above it. The line joining the charges is vertical, so the force on the central charge points upward. Option B would represent repulsion by a like charge, while the force is not zero because the charges are finite and separated. Thus option A is correct.

Correct answer: A. 2:1

Explanation: Coulomb’s law is F = k|Qq|/r². The target charge and the distance are identical for both interactions, so k, |q|, and r² cancel when the forces are divided. Consequently, the force ratio equals the ratio of the external-charge magnitudes: F₁/F₂ = |Q₁|/|Q₂| = 2/1. Hence the ratio is 2:1, making option A correct. The square factor affects distance, not charge in this comparison.

Correct answer: C. 10 N

Explanation: Net force is the vector sum of all forces acting on the object. When two forces point in the same direction, their magnitudes are added rather than subtracted. Therefore, F_net = 5 N + 5 N = 10 N, directed along the common direction of the two forces. Option C is correct. Zero would apply to equal opposite forces, while 25 N incorrectly multiplies the magnitudes.

Correct answer: C. 0 N

Explanation: The net force is obtained by vector addition. For two collinear forces acting in opposite directions, the resultant magnitude is the difference of their magnitudes: F_net = |5 N − 5 N| = 0 N. Because the forces are equal, they exactly cancel and no resultant direction remains. Hence option C is correct; 10 N would result from the same direction, and 25 N is not a valid force sum here.