Dipole in a Uniform External Field

The torque magnitude on an electric dipole in a uniform field is τ = pE sin θ, where p is the dipole moment, E is the electric-field strength, and θ is the angle between them. Thus the correct form is the product of p, E, and sin θ. Addition or subtraction has the wrong physical dimensions and structure, while charge divided by distance represents neither this torque nor its dependence on orientation. Hence A is correct.

The potential energy of an electric dipole in a uniform field is U = −pE cos θ. The cosine term expresses how the dipole is oriented relative to the field: it is −pE when parallel and +pE when antiparallel. Therefore the usual expression is based on the cosine of the angle between p and E. Distance squared, mass alone, and time alone are not the governing factors in this formula, so A is correct.

The governing concept is the force on a charge, F = qE. In a uniform field, both charges experience the same field magnitude. The positive charge feels a force along the field, while the negative charge feels an equal force opposite to the field. Thus the vector sum is F + (−F) = 0, so there is no net translational force, although a torque may still rotate the dipole. Therefore option A is correct; the other options incorrectly deny a force or rely on dipole size.

For a dipole in a uniform electric field, the potential energy is U = −pE cos θ. In the antiparallel position, θ = 180° and U = +pE, which is the maximum value. In the parallel position, θ = 0° and U = −pE, the minimum value. Hence the energy decreases by 2pE during the change. Option A is correct; it does not become infinite or remain constant.

The potential energy of a dipole is U = −pE cos θ. Initially, in the parallel position, θ = 0° and U_i = −pE. Finally, in the antiparallel position, θ = 180° and U_f = +pE. Therefore ΔU = U_f − U_i = 2pE > 0. For a slow rotation, the external agent must supply positive work equal to 2pE. Thus option A is correct.

A dipole consists of charges +q and −q separated by a fixed distance. In a uniform field E, the force on each charge has magnitude |q|E. The positive charge is pushed along E, whereas the negative charge is pushed opposite to E. Hence the two forces are equal in magnitude and opposite in direction. Their resultant force is zero, but their separated lines of action can produce torque. Therefore option A is correct.

For a dipole in a uniform electric field, the forces on +q and −q are equal and opposite, so the net force is zero. Their lines of action are separated, producing torque τ = pE sin θ. If the dipole is at an intermediate angle, such as 90°, sin θ is nonzero and the torque is nonzero. At 0° or 180°, torque vanishes. Therefore option A is correct; a zero field or parallel position cannot provide nonzero torque.

In a uniform electric field, the two opposite charges of a dipole experience equal forces in opposite directions. Because the forces act at two different points, their resultant is zero but their lines of action form a couple. The torque of this couple is τ = pE sin θ, which tends to rotate the dipole toward alignment with the field. Thus option A is correct; a single force would generally cause translation rather than pure dipole rotation.

The torque on an electric dipole is τ = pE sin θ, so equilibrium requires θ = 0° or 180°. Stability is determined by U = −pE cos θ. At θ = 0°, the potential energy is minimum, U = −pE, so a small displacement produces a restoring torque. At 180°, energy is maximum and equilibrium is unstable. Therefore stable equilibrium occurs at zero degrees, making option A correct.

For a dipole in a uniform electric field, equilibrium positions satisfy τ = pE sin θ = 0, giving θ = 0° or 180°. The potential energy U = −pE cos θ is maximum at θ = 180°, where U = +pE. A small displacement lowers the energy and produces a torque that moves the dipole farther from this orientation, so the equilibrium is unstable. Therefore option C, 180 degrees, is correct.

The torque magnitude on a dipole in a uniform electric field is |τ| = pE|sin θ|. It becomes zero when sin θ = 0, which occurs for θ = 0° or 180°. Thus a parallel orientation is certainly one possible zero-torque position; the antiparallel orientation is another, although it is not listed. A perpendicular dipole has maximum torque pE, not zero torque. Therefore option A is correct.

The electric dipole moment is defined as p = qd, where q is the magnitude of either charge and d is the displacement vector directed from the negative charge to the positive charge. Although its magnitude is qd, its direction is also physically meaningful. Therefore, it has both magnitude and direction and is a vector quantity. A scalar has magnitude only, so options B, C and D are not suitable.

For a dipole in a uniform electric field, the torque is given by τ = pE sin θ, where θ is the angle between the dipole moment and the field. This torque changes the dipole’s orientation and tends to reduce θ, lowering the potential energy U = −pE cos θ. Hence the dipole rotates toward alignment with the field. The torque does not reverse the field or remove charge.

The potential energy of an electric dipole in a uniform electric field is U = −pE cos θ, where θ is the angle between the dipole moment and the field. For a perpendicular dipole, θ = 90° and cos 90° = 0. Therefore U = 0 for the usual zero reference used in this formula. It is neither the minimum nor the maximum energy, which occur at 0° and 180°, respectively.

For a dipole in a uniform electric field, the potential energy is U = −pE cos θ. When the dipole is parallel to the field, θ = 0° and cos 0° = 1, so U = −pE, which is negative for positive p and E. This is the minimum-energy orientation and is stable. Positive energy corresponds to the opposite orientation, while zero occurs for a perpendicular orientation.

The potential energy of a dipole in a uniform electric field is U = −pE cos θ. In the opposite, or antiparallel, orientation, θ = 180° and cos 180° = −1. Consequently, U = +pE, so the usual potential energy is positive. This is the maximum-energy and unstable orientation. Negative energy belongs to the parallel position, while zero belongs to the perpendicular position.

Alignment means that the dipole’s orientation changes until its dipole moment points along the electric field. A change in orientation is a rotational effect, and the rotational effect of a force is called torque. For a dipole, τ = p × E, with magnitude pE sin θ, so the torque tends to reduce the angle between p and E. Mass, colour and temperature do not produce this alignment effect.

The governing idea is that the torque on an electric dipole is τ = pE sin θ and its potential energy is U = −pE cos θ, where θ is the angle between the dipole moment and the field. Therefore, the first useful step is to identify the dipole-moment direction and θ. Paper colour, question length, and diagram size do not affect the physics.

For a dipole carrying charges +q and −q in a uniform field E, the two charges experience forces of equal magnitude qE in opposite directions. Hence the vector sum is Fnet = qE − qE = 0. The forces may still form a couple and produce torque, but they do not produce a net translational force. Maximum, infinite, or field-equal force is therefore incorrect.

Zero net force means that the equal and opposite forces on the two charges cancel in translation. However, their lines of action are separated by the dipole length, so they form a couple. The resulting torque is τ = pE sin θ, which can rotate the dipole unless it is parallel or antiparallel to the field. Thus a rotational effect can remain even when net force is zero.

Electric dipole moment is defined as a vector quantity p = qd, where d is directed from the negative charge toward the positive charge. This convention is independent of the external electric field direction; the field only determines how the dipole experiences torque and energy changes. Therefore option A gives the standard direction, while option B reverses the definition and the other directions are not general.

For two equal and opposite charges +q and −q separated by distance d, the magnitude of the electric dipole moment is p = qd. Here q means the magnitude of either charge, not the algebraic net charge, because the total charge of the dipole is zero. Thus the charge–separation product is correct; adding field, using distance/time, or using field alone describes different quantities.

The magnitude of electric dipole moment is p = qd. Charge q has the SI unit coulomb (C), and separation d has the SI unit metre (m). Therefore the derived unit is C m, written as coulomb metre. Newton metre is a torque or energy unit, joule per coulomb is volt, and newton per coulomb is the unit of electric field, so none of those represents dipole moment.

The torque on an electric dipole in a uniform field is τ = pE sin θ, where θ is the angle between p and E. For fixed p and E, sin θ reaches its maximum value, 1, at θ = 90°. Hence τmax = pE when the dipole is perpendicular to the field. At 0° or 180° the torque is zero, and if E is zero no torque acts.

The torque magnitude on a dipole is τ = pE sin θ. When the angle θ is zero, the dipole moment is parallel to the electric field and sin 0° = 0. Therefore τ = pE × 0 = 0. This is not the maximum condition; maximum torque occurs at 90°. Infinite or half-maximum torque has no basis for θ = 0° under the stated ideal conditions.