Coulomb's Law (force between multiple charges)

Net force is the vector sum of all forces. Since the two forces act along the same straight line in opposite directions, their magnitudes are subtracted rather than added: Fnet = 14 N − 9 N = 5 N. The larger force points to the right, so the resultant is 5 N to the right. Adding them would incorrectly treat opposite forces as parallel in the same direction.

Forces in opposite directions must be combined algebraically with a sign convention. Taking right as positive, the net force is +8 N − 20 N = −12 N. The negative sign means the result points left, and its magnitude is 12 N. Therefore option A is correct. Adding 20 N and 8 N would be wrong because the forces oppose each other; zero would require equal magnitudes.

The principle of superposition says that forces are added as vectors. First combine the forces pointing right: 4 N + 6 N = 10 N rightward. Then oppose the 7 N leftward force: Fnet = 10 N − 7 N = 3 N. Because the rightward total is larger, the net force is 3 N to the right. The value 17 N incorrectly adds opposite directions.

For perpendicular vectors, the resultant magnitude is found using the Pythagorean relation R = √(F₁² + F₂²). Substitution gives R = √(6² + 8²) = √(36 + 64) = √100 = 10 N. Thus option B is correct. The value 14 N would be the simple arithmetic sum, which is valid only for forces in the same direction, while 48 N is their product.

When two forces are perpendicular, their resultant is not obtained by ordinary addition. Use R = √(F₁² + F₂²): R = √(9² + 12²) = √(81 + 144) = √225 = 15 N. Therefore option B is correct. The 21 N choice adds the magnitudes directly, and 108 N multiplies them; neither operation represents perpendicular vector addition.

The rightward and upward forces are mutually perpendicular, so their resultant follows the Pythagorean theorem. Its magnitude is R = √(12² + 5²) = √(144 + 25) = √169 = 13 N. Hence option B is correct. Subtracting gives 7 N only for opposite collinear directions, while 17 N incorrectly adds perpendicular magnitudes and 60 N is their product.

Coulomb’s law gives the magnitude of either force as F = kq²/r² because all three charges have the same magnitude. For a selected corner, each of the other two charges is located at the same side length r from it. Substituting the same q and the same r gives identical force magnitudes. Their directions differ, but that does not change their individual magnitudes. Thus A is correct; the other choices contradict the equal geometry or finite separation.

The governing concept is symmetry combined with vector superposition. Each corner charge is the same distance from the square’s centre, so each exerts a force of equal magnitude on the positive target. The force from one corner is cancelled by the force from the diagonally opposite corner, because the two directions are opposite. The same cancellation occurs for the other pair. Therefore the vector sum is zero, making A correct; no preferred direction remains.

Coulomb’s law determines the magnitude of each force, while superposition determines the net result. The left and right corner charges have equal magnitudes and equal distances from the central positive charge, so they exert equal repulsive forces. The left charge pushes the target to the right, while the right charge pushes it to the left. These equal opposite vectors cancel, giving zero net force. Thus A is correct, not a horizontal or vertical direction.

The governing concept is vector addition of forces, using a common positive direction. Take right as positive: the two rightward forces give 5 + 7 = 12 N, while the leftward force is −10 N. Therefore, the net force is 12 − 10 = +2 N. The positive sign means the result acts to the right. Option B reverses the direction, option C adds opposing forces directly, and option D incorrectly assumes complete cancellation.

The governing principle is algebraic vector addition. Choose right as positive. The two leftward forces combine to −(8 + 6) = −14 N, and the rightward force contributes +20 N. Thus the net force is +20 − 14 = +6 N, so it acts to the right. Option B has the correct magnitude but wrong direction; option C adds all magnitudes without considering direction, while option D ignores the unbalanced 6 N remainder.

For perpendicular forces, the resultant is found by the Pythagorean relation R = √(F₁² + F₂²), because the two vectors form the perpendicular sides of a right triangle. Substituting the values gives R = √(15² + 8²) = √(225 + 64) = √289 = 17 N. Option A is the difference, option C is the simple sum, and option D is not the correct product or vector result.

The rightward and upward forces are perpendicular, so their resultant magnitude follows R = √(Fₓ² + Fᵧ²). Using the given components, R = √(24² + 7²) = √(576 + 49) = √625 = 25 N. Option A is the difference of the components, option C is their arithmetic sum, and option D is their product, none of which represents the magnitude of perpendicular vector addition.

By Coulomb’s law, each force on the selected positive charge acts along the line joining it to the source charge. In an equilateral triangle, the angle between the two lines from one vertex to the other two vertices is the interior angle of the triangle. Every interior angle of an equilateral triangle is 60°, so the angle between the two repulsive force vectors is 60°. The other choices are not the triangle’s vertex angle.

Coulomb’s law gives the magnitude of each pairwise force as F = k|q₁q₂|/r². For the selected corner charge, the two source charges are equal, and both are at the same distance because all sides of an equilateral triangle are equal. Thus both interactions have identical values of kq²/r². The forces point in different directions, but their magnitudes are equal; therefore option A is correct.

Coulomb’s law is F = k|q_target q_source|/r². The target charge, the constant k, and the distance r are the same for both interactions. Consequently, only the external charge magnitude changes, and force is directly proportional to that magnitude. If the source charges are in the ratio 5:2, their force magnitudes are also in the ratio 5:2. Thus option A is correct; squaring the charge ratio would be inappropriate because the inverse square applies to distance.

The resultant is found by adding force vectors component by component. The eastward component is positive horizontally, while the southward component is downward vertically. Since both components are nonzero, the resultant lies between east and south, in the south-east quadrant. Its magnitude would be √(12² + 9²) = 15 N, but only the direction is asked. Therefore option B is correct; the other quadrants contain a wrong sign for at least one component.

The governing concept is vector addition of perpendicular forces. East and north are at 90°, so the resultant magnitude follows the Pythagorean relation R = √(F₁² + F₂²). Substituting the values gives R = √(33² + 56²) = √(1089 + 3136) = √4225 = 65 N. Therefore option B is correct. Adding 33 and 56 directly would incorrectly ignore the perpendicular directions.

The direction of a resultant is found by adding force vectors component by component. One component points west and the other points south, so the resultant must lie between those two directions, in the southwest quadrant. Its exact angle would satisfy tan θ = 14/48 measured south of west, but the magnitude is unnecessary for choosing the quadrant. Therefore option B, southwest, is correct; the other diagonal choices contain a northward or eastward component not present in the given forces.

Rightward and upward forces are perpendicular, so their resultant is calculated with the Pythagorean theorem rather than ordinary addition or subtraction. R = √(36² + 27²) = √(1296 + 729) = √2025 = 45 N. Hence option B is correct. The value 63 N is the simple sum and would apply only if both forces acted in the same direction; 9 N is their difference, not the perpendicular resultant.

The governing concept is vector addition of perpendicular force components. First, the eastward and westward forces oppose each other, so their resultant is 52 − 28 = 24 N eastward. This 24 N component is perpendicular to the 7 N northward component. Therefore, F = √(24² + 7²) = √625 = 25 N. Thus option A is correct; simple addition gives 87 N and ignoring the horizontal component gives 7 N, both of which are inappropriate.

Use vector addition by resolving forces along perpendicular directions. The northward and southward forces oppose one another, leaving 45 − 20 = 25 N northward. The remaining 25 N is perpendicular to the 60 N westward force. Hence F = √(25² + 60²) = √4225 = 65 N. Option A is correct. Adding all magnitudes would ignore directions, while 25 N ignores the westward component.

The governing principle is superposition of vectors. Two equal forces in exactly opposite directions have equal magnitudes but opposite signs, so their vector sum is zero. The only uncancelled contribution is the third force, which points northward. Consequently, the net force also points northward, making option A correct. It is not zero because the third force remains, and it cannot point south or east without a corresponding component.

When two force vectors are perpendicular, their resultant magnitude follows the Pythagorean theorem: R = √(F₁² + F₂²). Substituting the given values gives R = √(28² + 45²) = √(784 + 2025) = √2809 = 53 N. Hence option C is correct. The difference 45 − 28 gives 17 N only for opposite collinear forces, while 73 N is the magnitude sum for parallel forces.

For perpendicular force components, the resultant is obtained from R = √(F₁² + F₂²), not by ordinary addition or subtraction. Here R = √(11² + 60²) = √(121 + 3600) = √3721 = 61 N. Therefore option A is correct. The value 69 N is the direct sum, 49 N is an inappropriate difference, and 660 N is the product rather than a vector resultant.