Coulomb's Law (force between multiple charges)

Correct answer: C. Both charge and distance

Explanation: The relevant Coulomb expression is F = k|qouter qmiddle|/r². A larger charge tends to increase the force, whereas a greater distance decreases it according to the inverse square. Therefore neither charge alone nor distance alone is sufficient; their combined quantitative effect must be compared. The sign determines attraction or repulsion, but not the magnitude by itself. Hence C is correct.

Correct answer: A. Individual forces may exist but cancel each other

Explanation: The governing concept is the vector addition of electric forces. Each surrounding charge can exert a separate Coulomb force on the middle charge. If these forces have equal magnitudes and opposite directions, their vector sum is zero, even though the individual forces are present. Therefore option A is correct. Option B is not necessary, option C would make the simple law inapplicable, and option D would normally produce a larger nonzero resultant.

Correct answer: A. The direction of the separate force due to each charge

Explanation: The governing method is superposition of electrostatic forces. First identify the target charge and determine the magnitude and direction of the force produced by every other charge. Only after drawing or assigning these vectors should they be added to obtain the net force. Thus option A is correct. A final answer cannot be found reliably without the separate contributions; the farthest charge is not automatically the only important one, and forces cannot all be assumed zero.

Correct answer: B. In the denominator

Explanation: Coulomb's law is F = k|q₁q₂|/r². The distance r is squared and appears in the denominator, so the force is inversely proportional to r². For example, if the separation is doubled while charges remain fixed, the force becomes one-fourth. Therefore option B is correct. It is not a numerator factor, a unit-only feature, or a direction term; direction is handled separately by attraction or repulsion.

Correct answer: B. Charges with larger magnitudes

Explanation: For two point charges, Coulomb's law gives F = k|q₁q₂|/r². When r is the same for all comparisons, k/r² is constant, so the force depends on the product of the charge magnitudes. Larger magnitudes generally produce a larger product and hence a greater force, making option B correct. A zero charge gives zero force, smaller charges give less force, and equal distance alone does not make all forces equal.

Correct answer: B. By vector addition

Explanation: Force is a vector quantity, so both magnitude and direction must be considered. Perpendicular forces cannot generally be combined by ordinary scalar addition or subtraction. If their magnitudes are F₁ and F₂, the resultant magnitude is √(F₁² + F₂²), and its direction is found from the components, such as tan θ = F₂/F₁. Therefore option B is correct; the resultant is not automatically zero.

Correct answer: A. Toward the left

Explanation: Use attraction and repulsion together with the charge positions. The left negative charge attracts the middle positive charge toward the left. The right positive charge repels the middle positive charge away from the right-hand charge, which is also toward the left. Thus both individual forces point left, so option A is correct. Equal distances affect their magnitudes, but the direction conclusion follows from the signs and positions.

Correct answer: B. Toward the right

Explanation: The left positive charge repels the middle positive charge, pushing it away from the left and therefore toward the right. The right negative charge attracts the middle positive charge toward itself, also toward the right. Consequently both Coulomb forces have the same rightward direction, so option B is correct. Equal distances may make the magnitudes equal if the outer charge magnitudes are equal, but they do not reverse the direction.

Correct answer: C. Zero

Explanation: Each outer positive charge attracts the middle negative charge. The left charge pulls it leftward, while the right charge pulls it rightward. Because the outer charges have equal magnitudes and equal distances from the middle, Coulomb's law gives equal force magnitudes, k|qQ|/r², in opposite directions. Their vector sum is therefore zero, so option C is correct. The symmetry, not the negative sign alone, produces cancellation.

Correct answer: A. Zero

Explanation: All three charges are negative, so each outer charge repels the negative middle charge. The left outer charge pushes the middle charge to the right, while the right outer charge pushes it to the left. Equal outer magnitudes and equal distances make these forces equal in magnitude, k|qQ|/r². Since they are opposite vectors, they cancel and the net force is zero; therefore option A is correct.

Correct answer: B. Toward the right

Explanation: Choose right as the positive direction. If the rightward force is Fᵣ and the leftward force is Fₗ, the net force is F_net = Fᵣ − Fₗ. Since Fᵣ > Fₗ, this difference is positive, so the resultant points to the right. Therefore option B is correct. The net force would be zero only if the two opposite forces were equal; a larger leftward force would reverse the direction.

Correct answer: A. Toward left

Explanation: The net force is the vector sum of all individual forces. When two forces act in opposite horizontal directions, subtract the smaller magnitude from the larger one and keep the direction of the larger force. Since the leftward force is greater, the resultant is nonzero and points left. It is not rightward, zero, or upward.

Correct answer: C. Zero

Explanation: Net force is obtained by adding forces as vectors, including their directions. An upward force and an equal downward force lie along the same line but point oppositely, so their signed sum is F + (−F) = 0. Therefore the charge has zero net force. The forces do not become double because they oppose and cancel each other.

Correct answer: B. Comparison of total upward and downward magnitudes

Explanation: Force is a vector, so both magnitude and direction must be considered. First add the magnitudes of the two upward forces, then compare that total with the downward force. The larger total determines the net direction, while their difference gives the net magnitude; equal totals would give zero. Merely counting forces is insufficient.

Correct answer: B. Distance

Explanation: Coulomb's law is F = k|q₁q₂|/r². With the charges and medium fixed, increasing the separation r increases the denominator, so the force decreases according to the inverse-square relation. Increasing either charge or their product would increase the force, while k is fixed for a specified medium. Therefore distance is the correct choice.

Correct answer: B. Magnitudes of the charges

Explanation: Coulomb's law gives F = k|q₁q₂|/r². For fixed separation and medium, increasing either charge increases the product |q₁q₂|, so the electrostatic force increases in direct proportion to that product. Distance and its square appear in the denominator, so increasing them reduces the force; time does not appear in this law. Hence option B is correct.

Correct answer: A. Whether the force is attractive or repulsive

Explanation: In Coulomb's law, the signs of the two charges determine the nature of their interaction. Like charges, such as positive-positive or negative-negative, repel each other, whereas unlike charges attract. The signs do not determine the unit of force or distance, and charge has no physical colour. Thus option A correctly identifies what the sign relation tells us.

Correct answer: B. No, forces may act but cancel

Explanation: The net force is the vector sum of all individual forces, not a statement that each force is absent. Forces from different charges can have equal magnitudes and opposite directions, producing a resultant of zero. The charge can therefore still experience separate electric forces. Option A is false, and zero net force is not infinite or evidence that the charge does not exist.

Correct answer: A. Ignoring direction

Explanation: Every electric force is a vector, so its direction must be identified before adding it to other forces. Ignoring direction treats all magnitudes as ordinary positive numbers and can give a wrong resultant; opposite forces may need subtraction rather than addition. Identifying distance, using the charge unit, and reporting force in newtons are not mistakes when done correctly. Therefore A is correct.

Correct answer: A. Magnitudes of the charges

Explanation: For two point charges, Coulomb's law is F = k|q₁q₂|/r². If the medium is fixed, k is unchanged, and if the separation is fixed, r² is unchanged. The remaining relevant variable is the product of the charge magnitudes. Changing either charge can therefore change the force; clock time, colour, and table height do not occur in this electrostatic relation.

Correct answer: A. Product of both charges

Explanation: Coulomb's law states F = k|q₁q₂|/r², so the force depends on the product of the magnitudes of both charges, not on just the larger or smaller charge. With the same distance and medium, k/r² is fixed, leaving F proportional to |q₁q₂|. Thus both charges contribute, even when one is much larger than the other, making option A correct.

Correct answer: A. The directions may reverse

Explanation: By Coulomb’s law, the magnitude of each force depends on the product of the interacting charges, while its direction is determined by attraction or repulsion. Reversing the sign of the target charge reverses the sign of every charge product involving it. Thus an attractive interaction can become repulsive, or vice versa, so the corresponding force directions may reverse. Distance does not automatically change, and the force is not necessarily zero.

Correct answer: A. Find each force’s magnitude and direction separately, then add them vectorially

Explanation: The governing principle is superposition: the net Coulomb force is the vector sum of the separate forces exerted by all other charges on the target charge. Therefore, calculate each contribution using F = k|qQ|/r², determine its direction from attraction or repulsion, resolve components if necessary, and then add vectors. Direct scalar addition, ignoring directions, or dropping a small charge can produce an incorrect result.

Correct answer: B. Attractive

Explanation: Coulomb’s law gives the magnitude of the electrostatic force, while the signs of the charges determine whether the interaction is attractive or repulsive. Opposite signs have a negative charge product, so the charges attract each other along the line joining them. The force is not automatically zero; its magnitude becomes zero only if a charge is zero or in a special net-force cancellation situation. Friction is unrelated.

Correct answer: B. Repulsive

Explanation: For two charges with the same sign, the product q₁q₂ is positive. Coulomb’s law therefore describes a repulsive electrostatic interaction: each charge pushes the other away along the line joining them. This applies to both positive–positive and negative–negative pairs. The force is not generally zero, and it is not merely gravitational; gravity may also exist, but the question concerns the electric force.