Coulomb's Law (force between multiple charges)

The direction of a resultant vector is determined by its components. A southward component points downward on a map, and a westward component points left. Adding these perpendicular components places the resultant between south and west, specifically in the south-west quadrant. The magnitudes affect the angle, not the quadrant. Therefore option D is correct; the other directions contain a wrong sign for at least one component.

For two equal forces F making an angle θ, the resultant is R = √(F² + F² + 2F²cosθ). At θ = 0°, cosθ = 1, so R = √(4F²) = 2F. Physically, both forces point in exactly the same direction and therefore add directly. Option B is correct; zero would apply to equal opposite forces at 180°, not to parallel forces.

The governing principle is superposition and vector cancellation. Two forces with equal magnitudes in exactly opposite directions have a vector sum of zero. They therefore cancel completely, leaving only the third force. Because that remaining force points southward, the net force also points southward. Option B is correct. The result is not zero because the third force is still present; north and east contradict its stated direction.

A resultant is the vector sum of all component forces. The westward component points left on a map, and the southward component points downward. Their sum must lie between these two directions, namely in the south-west quadrant. The 80 N component is larger, so the direction is closer to west, but it remains south-west. Hence option B is correct; the other diagonal choices contain either an incorrect northward or eastward component.

The governing concept is vector cancellation. An angle of 180° means the two force vectors point in exactly opposite directions. Since their magnitudes are equal, we may write F₁ = F and F₂ = −F. Their vector sum is therefore Fnet = F + (−F) = 0. Option B is correct. Same-direction forces would add, force is a vector rather than a scalar, and zero distance is irrelevant to this cancellation.

The governing rule is vector superposition. The two equal opposite forces have vectors F and −F, so their sum is zero. They cancel completely and leave only the third force. Since that remaining force points westward, the net force also points westward. Option B is correct. The result is not zero because the third force has not been cancelled; east and north are inconsistent with the stated direction of the remaining force.

Use the interaction rule for charges. The positive charge above repels the positive target, pushing it downward. The negative charge below attracts the positive target, also pulling it downward. Because both source charges have equal magnitude and equal distance from the target, the two force magnitudes are equal; more importantly, their directions are the same. They therefore add rather than cancel. The net force is downward, so option B is correct.

The negative charge above the negative target produces repulsion, so it pushes the target downward. The positive charge below attracts the negative target, pulling it downward toward itself. Thus both electrostatic forces point downward. Equal distances and equal magnitudes ensure equal force magnitudes, but cancellation does not occur because the directions are identical. The resultant force is consequently downward, making option B the only correct answer.

The magnitude of electric dipole moment is p = qd. In the SI system, charge q is measured in coulombs and separation d is measured in metres. Multiplying these units gives coulomb metre, written C m. Newton is a unit of force, joule is a unit of energy, and newton per coulomb is a unit of electric field. Therefore option A is correct.

The governing concept is electrical conductivity. Metals contain mobile conduction electrons, so an excess charge can move over their surface and redistribute when an electric field is present. In an insulator, electrons are tightly bound to atoms or molecules, so charge generally remains localized, apart from limited polarization. Thus option A is correct. Options B and D reverse or erase the material difference, while C is false because conductors can retain surface charge.

The governing relation between force, charge, and electric field is F = qE. Rearranging gives q = F/E. Substituting the supplied values, q = 4 N divided by 2 N C⁻¹ = 2 C. Because the test charge is explicitly positive, the result is +2 coulombs. Therefore option A is correct; the other numerical choices do not satisfy F = qE for the stated field.

Electric field lines represent the direction in which a positive test charge would move. By definition, lines originate from a positive charge and terminate on a negative charge, or extend to infinity if no opposite charge is present. Therefore, for an electric dipole, the external field lines generally run from +q to −q. They are not closed circles, and their direction is not reversed.

The torque on a dipole in a uniform electric field is τ = pE sinθ. It is a turning effect that changes the angle θ between the dipole moment p and the field E, tending to align the dipole with the field. Thus option A is correct. Torque changes orientation, not the charge unit, surface colour, or time; translational motion is associated with net force rather than torque.

The direction of an electric field at any point is defined as the direction of force on a small positive test charge. Field lines therefore originate from positive charges and terminate on negative charges; in a dipole diagram, they generally run from the positive charge toward the negative charge. Thus option A is correct. They do not generally begin at negative charges, connect positive charges, or form closed circles as electrostatic field lines.

For a dipole in a uniform electric field, the torque magnitude is τ = pE sin θ. At θ = 90°, sin 90° = 1, so τ = pE, the greatest possible value for fixed p and E. Hence the torque is maximum and option A is correct. It is zero at 0° and 180°, not at 90°. The sign of torque depends on the chosen rotational convention, so “always negative” is not valid.

The torque magnitude is |τ| = pE sin θ. Between 0° and 90°, sin θ increases continuously from 0 to 1. Therefore, for fixed p and E, the torque magnitude increases continuously and reaches its maximum value pE at 90°. Option A is correct. The signed direction may be discussed separately, but the question asks for magnitude, so option D is not appropriate.

For a dipole in a uniform electric field, |τ| = pE sin θ. At 90°, sin θ = 1, so the torque magnitude is maximum, pE. At 180°, sin θ = 0, so the torque magnitude is zero. As θ increases through this interval, sin θ decreases from 1 to 0; therefore the torque magnitude decreases. Option A is correct.

The torque on a dipole in a uniform electric field is τ = pE sinθ. For fixed p and E, the largest possible value of sinθ is 1, which occurs at θ = 90°. Therefore the dipole moment must be perpendicular to the electric field, making option A correct. At 0° and 180°, sinθ is zero and the torque vanishes; 30° gives only an intermediate value.