Coulomb's Law (force between multiple charges)

For fixed charges, Coulomb’s law gives F ∝ 1/r². Tripling the separation changes r to 3r, so the squared distance becomes (3r)² = 9r². Consequently, the force becomes one-ninth of its original value. The new force is 27/9 = 3 N. Therefore option A is correct. The 9 N option would correspond to dividing by three rather than by the square of three.

With unchanged charges, Coulomb’s law gives F ∝ 1/r². Replacing r by r/3 makes the squared distance r²/9, so the force increases by a factor of 9. Therefore the new force is 9 × 5 N = 45 N. Option B is correct. The value 15 N results from multiplying by only three, while 5/3 N and 5/9 N incorrectly predict a decrease when the separation is reduced.

Coulomb’s law states that the magnitude of force is F = k|q₁q₂|/r². When each charge is halved, the product q₁q₂ becomes (q₁/2)(q₂/2) = q₁q₂/4. Since the distance is unchanged, the denominator does not change. Therefore the new force is 20/4 = 5 N, so option B is correct. Option A would result from halving only one charge.

The governing concept is electrostatic repulsion: two charges with the same positive sign push one another away. The upper charge repels the positive charge at the centre along the vertical line joining them. Thus the centre charge is pushed away from the top, namely downward. The left and right charges are irrelevant because the question asks specifically for the force due to the upper charge; zero would describe no force, not this repulsion.

The principle used is superposition of electrostatic forces. The equal charges on the left and right exert equal repulsive forces in opposite horizontal directions, so their vector sum is zero. The upper positive charge still repels the central positive charge away from itself, producing a downward force. Hence the net force is downward, option B. It is not zero because the vertical force has not been cancelled.

Force is a vector quantity, so both magnitude and direction must be considered. For two forces acting at an angle, their resultant can be found by vector addition, commonly through components or the parallelogram law. Merely adding magnitudes is valid only when they act in the same direction. Choosing the smaller force or setting both to zero has no physical basis. Therefore option A is correct.

Coulomb’s law gives F = k|Qq|/r². For the same target charge, the relevant comparison is the source-charge magnitude divided by the square of its distance, or |Q|/r². A large charge can still produce a smaller force if it is sufficiently far away, and a nearby small charge may dominate. The sign determines attraction or repulsion, not force magnitude. Thus option A is correct.

For equal source charges and the same target charge, Coulomb’s law reduces to F ∝ 1/r². Let the distances be r and 2r. Then the nearer force is proportional to 1/r², while the farther force is proportional to 1/(2r)² = 1/(4r²). Therefore F_near:F_far = 1 : 1/4 = 4:1. The inverse-square relation makes the nearer force four times larger, so option C is correct.

Use F = k|Qq|/r² and compare the first interaction with the second. The charge factor is Q₁/Q₂ = 4, while the distance factor contributes (r₂/r₁)² = (1/2)² = 1/4 because the first charge is twice as far away. Thus F₁/F₂ = 4 × 1/4 = 1. The two force magnitudes are equal, so option B is correct.

The vector-cancellation condition is strict: two forces produce zero resultant only when they have equal magnitudes and point in exactly opposite directions. Equal magnitudes alone are insufficient. If the angle between them is not 180°, their vector sum has a nonzero component, so a net force remains. The sign of the target charge does not change this cancellation condition, and equal distances are irrelevant by themselves. Therefore option B is correct.

The governing concept is Coulomb’s law: like charges repel and unlike charges attract. Initially, attraction proves that the two charges have opposite signs. Reversing the sign of only one charge makes both charges have the same sign, while their magnitudes and separation remain unchanged. Therefore, the force changes from attraction to repulsion, so option B is correct; it does not become zero or directionless.

Coulomb’s law states that charges with the same sign repel, whereas charges with opposite signs attract. Since the original force is repulsive, the two original charges have the same sign. Reversing only one sign makes the charges opposite in sign, so their interaction becomes attractive. The charge magnitudes and distance have not been specified to change, so option B is the only correct answer.

The nature of Coulomb force depends on whether the two charges have like or unlike signs. Reversing both signs together preserves that relationship: (+,+) becomes (−,−), and (+,−) becomes (−,+). Thus like charges remain like and unlike charges remain unlike. The force therefore keeps the same attractive or repulsive nature, while the stated magnitude also remains unchanged. Option A is correct.

Coulomb’s law in a medium is commonly written as F = (1/4π ε) |q₁q₂|/r², where ε is the permittivity of the medium. Even if the charges and separation r stay fixed, changing ε changes the force magnitude. In an ordinary dielectric medium, greater permittivity generally reduces the force compared with vacuum or air. Thus option A is correct; the direction need not change.

The governing idea is the permittivity of the medium. For fixed charges and separation, Coulomb’s law gives F = (1/4π ε) |q₁q₂|/r². A medium with a larger permittivity ε reduces the electric interaction compared with air or vacuum, so the force magnitude becomes smaller. The charges do not disappear, the distance does not become zero, and force remains a vector. Therefore option A is correct.

The principle of superposition says that the net electric force on a selected target charge equals the vector sum of the individual electric forces exerted on that target by every other charge. We do not add forces acting on unrelated charges, nor do we directly include interactions between the external charges. Therefore option A identifies exactly the required forces. Their directions must be considered during vector addition.

For each external charge, Coulomb’s law gives F_i = (1/4π ε) |Qq_i|/r_i². With the external charge q_i, distance r_i, and medium fixed, the force is directly proportional to the target charge Q. Replacing Q by 2Q therefore changes every individual force to 2F_i. The directions are unchanged if only the magnitude is doubled, so option A is correct.

For an external charge q, the force magnitude is proportional to |Qq|/r², so changing only the sign of target charge Q does not alter the magnitude. However, the vector force is proportional to Qq; changing Q to −Q reverses the force vector. Thus attraction becomes repulsion or repulsion becomes attraction for every external charge. Option A is correct, while the other choices incorrectly change the magnitude.

The governing concept is vector addition of forces. Net force is the vector sum of all individual forces, so a zero result means that the forces balance in magnitude and direction; it does not mean that every force is absent. For example, equal opposite electric forces can act simultaneously on a charge. Therefore option A is correct. Option B confuses zero resultant with zero individual forces, while C and D are unnecessary and physically inappropriate conditions.

For several charges, Coulomb's law must be applied separately to each source charge and the resulting forces must then be added as vectors. First identify the target charge, because the requested net force acts on that charge. Next calculate each force using its charge values and separation, assign its correct direction, and finally resolve components or add vectors. Thus option A is correct; B ignores direction, C omits charge effects, and D ignores other forces.

Coulomb's law gives F = k|q₁q₂|/r², so with unchanged charges the force varies inversely as the square of separation. If r becomes 2r, the new force is F' = F/(2²) = 32/4 = 8 N. Therefore option A is correct. Option B would result from incorrectly using an inverse first-power relation, while C and D incorrectly predict an increase when the distance is increased.

Coulomb's law states F = k|q₁q₂|/r². Since the distance is unchanged, multiplying q₁ by 3 and q₂ by 3 multiplies their product by 3 × 3 = 9. Hence F' = 9F = 9 × 12 = 108 N, so option C is correct. Option A considers only one charge change, B uses an incorrect factor of six, and D represents a decrease unsupported by the law.

The governing relation is F = k|q₁q₂|/r². With distance fixed, force is directly proportional to the product q₁q₂. Doubling one charge contributes a factor of 2, and tripling the other contributes a factor of 3; together the factor is 2 × 3 = 6. Therefore option C is correct. Options A and B include only one change, while D incorrectly squares or otherwise overcounts the charge factors.

Use Coulomb's law F = k|q₁q₂|/r². Doubling one charge multiplies the numerator, and therefore the force, by 2. Doubling the distance changes r² to (2r)² = 4r², reducing the force by a factor of 4. The combined factor is 2 × 1/4 = 1/2, so the new force is half the original. Hence option A is correct; the other choices omit or mishandle one factor.

Coulomb's law is F = k|q₁q₂|/r². Doubling both charges makes the charge product 2 × 2 = 4 times larger. Halving the distance changes r² to (r/2)² = r²/4, which makes the force 4 times larger again. Thus the total factor is 4 × 4 = 16, so option C is correct. A includes only the charge effect, B misses one factor of two, and D ignores both changes.