Dipole in a Uniform External Field

The rightward and upward forces are perpendicular components of the net force. Therefore use R = √(Fₓ² + Fᵧ²) = √(8² + 6²) = √(64 + 36) = √100 = 10 N. Option A is correct. Fourteen is the arithmetic sum, two is the difference, and forty-eight is the product; these operations ignore the perpendicular vector nature of the forces.

For a dipole in a uniform electric field, the positive charge experiences a force qE in the field direction, while the negative charge experiences an equal force qE in the opposite direction. Their vector sum is therefore zero, so option A is correct. The dipole can still experience a torque, τ = pE sin θ, when its axis is not aligned with the field. Thus zero net force does not imply zero rotational effect; the other options are not generally valid.

The torque on an electric dipole in a uniform field is τ = pE sin θ, where θ is the angle between the dipole moment and the electric field. For fixed p and E, sin θ has its greatest value, 1, at θ = 90°. Hence the torque is maximum when the dipole is perpendicular to the field, making option B correct. At 0° or 180° the torque is zero, and a zero field also produces no torque.

Torque is the turning effect of a force. In a uniform electric field, the two equal and opposite forces on the dipole act along parallel but generally different lines of action, forming a couple. Its torque is τ = pE sin θ, which tends to rotate the dipole so that its dipole moment aligns with the field. Therefore option A is correct. The torque does not destroy the dipole, cancel the field, or remove either charge.

The potential energy of a dipole in a uniform electric field is U = −pE cos θ. It is minimum when cos θ = 1, which occurs at θ = 0°, meaning the dipole moment is parallel to the field. A small angular displacement then produces a restoring torque, so this position is stable. Therefore option A is correct. The opposite orientation has maximum energy and is unstable, while removing the dipole is not an equilibrium position of the given system.

For a dipole in a uniform electric field, U = −pE cos θ. At θ = 180°, the dipole moment is opposite to the field and U reaches its maximum value, +pE. A slight angular displacement lowers the energy and produces a torque that moves the dipole farther from this orientation, so the equilibrium is unstable. Hence option C is correct. Parallel alignment is stable, while a weak field changes the torque magnitude but does not define unstable equilibrium.

A dipole consists of charges +q and −q with equal magnitudes separated by a small distance. In a uniform field, the field strength is the same at both charge locations, so the forces have equal magnitudes qE but opposite directions. Their vector sum is therefore zero, making option A correct. The dipole does contain charges, and the electric field acts on both, although their separated lines of action can still produce torque.

For a dipole in a uniform electric field, the torque is given by τ = pE sin θ, where p is the dipole moment, E is the field magnitude, and θ is the angle between them. The sine is zero at θ = 0° and 180°. Hence the torque is zero when the dipole is parallel or antiparallel to the field. Perpendicular orientation gives maximum torque, not zero torque.

The potential energy of a dipole in a uniform electric field is U = −pE cos θ. For a fixed p and E, the minimum value occurs when cos θ = 1, that is, θ = 0°. Therefore the dipole must be parallel to the field, giving Umin = −pE. At 90° the energy is zero, while the antiparallel position gives maximum energy +pE.

For a dipole in a uniform field, U = −pE cos θ. With p and E fixed, energy is greatest when cos θ = −1, which occurs at θ = 180°. Thus the dipole is antiparallel to the field and Umax = +pE. The parallel position gives minimum energy, and the perpendicular position gives U = 0, so neither A nor B is correct.

The torque on a dipole is τ = pE sin θ, and its action tends to reduce the potential energy U = −pE cos θ. Consequently, the dipole rotates so that its dipole moment becomes aligned with the external electric field. The parallel orientation is stable and has minimum energy. Antiparallel orientation is unstable, while cancelling the field or random motion is not the governing effect.

The torque on an electric dipole is τ = pE sin θ, where θ is the angle between the dipole moment and the electric field. For a parallel dipole, θ = 0°, so sin 0° = 0 and therefore τ = 0. Maximum torque occurs at 90°, not at 0°. Thus the correct answer is zero; the values half, maximum, and infinite do not follow from the formula.

For a dipole in a uniform field, τ = pE sin θ. When the dipole is opposite to the field, the angle is θ = 180°, and sin 180° = 0. Hence the torque is zero, although this orientation is an unstable equilibrium and the potential energy is maximum. Maximum torque occurs at 90°, so option B confuses energy behaviour with torque.

The magnitude of torque on an electric dipole in a uniform field is τ = pE sin θ. At θ = 90°, sin 90° = 1, so τ = pE, which is the maximum possible magnitude for fixed p and E. The torque is not zero in this orientation; zero values occur at 0° and 180°. Its vector direction depends on the orientation, but its magnitude is maximum.

A dipole contains equal and opposite charges separated by a distance. In a uniform electric field, the positive charge experiences a force along the field and the negative charge experiences an equal force opposite to the field. Their resultant force is zero, but their parallel and separated lines of action form a couple, producing torque τ = pE sin θ. Thus A is correct.

In a uniform electric field, the forces on the positive and negative charges of a dipole are equal in magnitude and opposite in direction. Therefore the net translational force is zero. Since the forces act at different points, however, they form a couple and produce torque τ = pE sin θ. The principal effect is rotation or alignment; mass does not change and there is not always no effect.

The torque magnitude is τ = pE sin θ. If the dipole moment p and angle θ remain fixed, then τ is directly proportional to the electric-field magnitude E. Therefore increasing E increases the torque in the same proportion, except that when sin θ = 0 the torque remains zero for every E. Under the usual nonzero-angle condition, option A is correct.

For an electric dipole in a uniform field, the torque magnitude is given by τ = pE sin θ, where p is the dipole moment, E is the field strength, and θ is the angle between them. Since E and θ remain unchanged, τ is directly proportional to p. Thus increasing p increases the torque by the same proportion. The other choices are incorrect because the torque does not automatically vanish or lose direction.

The potential energy of a dipole in a uniform electric field is U = −pE cos θ. Therefore it depends on the dipole moment p, field strength E, and especially the orientation represented by the angle θ between p and E. Among the given choices, only the angle is relevant. Colour, temperature alone, and mass alone do not determine this electrostatic potential energy, so option A is correct.

The torque on a dipole is a vector given by τ⃗ = p⃗ × E⃗. The direction of a cross product is perpendicular to the plane containing p⃗ and E⃗, and it is determined using the right-hand rule: curl the fingers from p⃗ toward E⃗, while the thumb gives the torque direction. The other listed rules do not determine this electrostatic vector direction.

In a uniform electric field, the equal and opposite forces on the positive and negative charges of a dipole give zero net force, so Newton’s second law gives Fnet = MaCM = 0. Hence the centre of mass has no translational acceleration. However, these forces may form a couple and produce torque pE sin θ, so rotation can still occur. Therefore A is the only correct statement.

The potential energy of a dipole is U = −pE cos θ. When the dipole is parallel to the field, θ = 0° and cos 0° = 1, so U = −pE, its minimum value for fixed p and E. This orientation is stable equilibrium because a small displacement produces a restoring torque. Thus A is correct; antiparallel orientation gives maximum, not minimum, energy.

For a dipole in a uniform electric field, U = −pE cos θ. In the opposite, or antiparallel, orientation, θ = 180° and cos 180° = −1; hence U = +pE, the maximum value for fixed p and E. This is unstable equilibrium because a small displacement leads the dipole away from that orientation. Therefore B is correct, while A describes the parallel stable state.

The torque on an electric dipole in a uniform field is τ = pE sin θ. If the dipole moment p is zero, the entire product is zero regardless of the field strength E or angle θ. Physically, p = 0 means there is no effective charge separation producing a dipole torque. Therefore the torque is zero, so option A is correct; it cannot become maximum, infinite, or double.

For a dipole in a uniform electric field, the torque magnitude is τ = pE sin θ. If the electric field strength E is zero, τ becomes zero for every value of the dipole moment p and every orientation θ. Equivalently, no external electric force acts on the dipole charges to form a torque-producing couple. Therefore A is correct; the torque is not maximum, equal to p, or necessarily negative.