Dipole in a Uniform External Field

The electric force on a charge is given by F = qE. A dipole consists of charges +q and −q, so both charges have the same magnitude |q|. In a uniform electric field, the field magnitude E is identical at the positions of both charges. Therefore each force has magnitude |q|E, although the force directions are opposite because the charges have opposite signs. The equal and opposite forces form a couple that produces torque. Thus option A is correct.

The governing idea is the force on each charge, F = qE. In a uniform field, the field has the same magnitude and direction at both charges, so the forces are equal and opposite; their resultant is zero, although they may produce torque. In a non-uniform field, the two charges generally experience different field strengths, so the forces do not cancel completely. Therefore option A is correct; the dipole moment does not vanish, and forces do act in a uniform field.

In a uniform electric field, the positive and negative charges of the dipole experience forces parallel to the field, with equal magnitudes and opposite directions. When the dipole is oblique, the charges are at different locations, so the two parallel lines of action are separated by a perpendicular distance. These forces therefore form a couple and produce torque, τ = pE sin θ. Hence option A is correct; the lines are not coincident, perpendicular, or curved.

For a dipole in a uniform field, the torque magnitude is τ = pE sin θ, where θ is the angle between the dipole moment and the field. In the parallel arrangement, θ = 0°, so sin 0° = 0 and τ = 0. Geometrically, the equal and opposite forces act along the same straight line, giving zero perpendicular separation and hence no couple. Therefore option A is correct.

The relevant approximation is quasi-static rotation. Kinetic energy is K = ½Iω², so when the dipole is rotated very slowly, its angular speed ω is made very small and K becomes negligible compared with the change in electrostatic potential energy. The electric field and dipole moment need not be zero, and the mass or moment of inertia is not assumed to vanish. Therefore option A is correct.

The electrostatic potential energy of a dipole is U = −pE cos θ. With p and θ fixed, cos θ is constant, so U changes linearly with the field magnitude E. Consequently, the magnitude |U| increases as E increases, except for the special case cos θ = 0, where U remains zero; the question’s general statement is therefore option A. The sign itself is determined by the angle.

For a dipole in a uniform field, U = −pE cos θ and the torque tends to reduce the potential energy. The torque magnitude is pE sin θ and its direction rotates the dipole toward the stable parallel orientation, θ = 0°. When θ is less than 90°, decreasing θ increases cos θ and makes U more negative, so the energy falls. Therefore option A is correct; rotation is not toward 180°.

The torque on an electric dipole in a uniform field is given by τ = pE sin θ, where θ is the angle between the dipole moment and the field. For a parallel arrangement, θ = 0°, so sin 0° = 0 and τ = 0. The forces on the two charges are equal and opposite and produce no turning effect. Thus option A is correct; maximum torque occurs at 90°.

For a dipole in a uniform electric field, the torque magnitude is τ = pE sin θ. When the dipole is perpendicular to the field, θ = 90° and sin 90° = 1, giving τ = pE, the largest possible value for fixed p and E. It is zero when parallel and smaller at intermediate angles. Therefore option A is correct.

A dipole contains equal and opposite charges separated by a small distance. In a uniform field, the forces qE on the two charges have equal magnitude and cancel, although they can produce torque. In a non-uniform field, the field magnitude differs at the two charge positions, so the forces need not be equal. Their vector sum can therefore be a nonzero net force. Option A is correct.

The torque on a dipole in a uniform electric field is τ = pE sin θ. At θ = 30°, sin 30° = 1/2, so τ = pE/2, which is nonzero when p and E are nonzero. Torque vanishes only for θ = 0° or 180°, when the dipole is parallel or antiparallel to the field. Thus option A is correct; the other options misinterpret charge neutrality or the angle dependence.

The potential energy of a dipole in a uniform field is U = −pE cos θ. At the antiparallel position, θ = 180° and U = +pE, which is a maximum, so the equilibrium is unstable. A small angular displacement produces a torque τ = pE sin θ that increases the displacement and tends to rotate the dipole toward alignment with the field. Thus option A is correct; the other choices are physically incorrect.

For a dipole in a uniform electric field, U = −pE cos θ. When the dipole moment is parallel to the field, θ = 0° and the potential energy is minimum, U = −pE. If the dipole is slightly rotated, the torque τ = pE sin θ acts in the direction that restores alignment with the field. Therefore the parallel orientation is stable equilibrium, making option A correct.

The governing concept is torque on an electric dipole. In a uniform field, the positive and negative charges experience forces of equal magnitude in opposite directions, so their vector sum, or net force, is zero. However, the forces act at two different points and therefore form a couple. This couple produces torque τ = pE sin θ, which can rotate the dipole unless it is already parallel or antiparallel to the field. Thus option A is correct; the other choices incorrectly deny the charge forces or the field.

The potential energy of an electric dipole in a uniform field is U = −pE cos θ, where θ is the angle between the dipole moment and the field. For alignment, θ = 0°, so U = −pE, the lowest possible value for fixed p and E. The dipole is therefore in stable equilibrium. Option A is correct; maximum energy occurs at 180°, not at 0°.

For a dipole in a uniform electric field, U = −pE cos θ. When the dipole moment is opposite to the field, θ = 180° and cos 180° = −1. Therefore U = −pE(−1) = +pE, which is the maximum value for fixed p and E. This is unstable equilibrium. Thus option A is correct, while minimum energy belongs to θ = 0°.

For a dipole, U = −pE cos θ. At stable equilibrium, θ = 0° and U = −pE; at unstable equilibrium, θ = 180° and U = +pE. The potential-energy increase is ΔU = 2pE. If the rotation is quasistatic, the external agent must supply work equal to this increase. Hence option A is correct; no charge or field needs to be removed.

A polar molecule has a permanent electric dipole moment p because its positive and negative charge centres are separated. In an external field E, the molecule experiences torque τ = pE sin θ, which tends to reduce the angle θ between p and E. The stable orientation is θ = 0, so the dipole tends to align with the field. It does not gain net charge or automatically break apart.

The torque on an electric dipole in a uniform field is τ = pE sin θ. When the dipole is perpendicular to the field, θ = 90°, so the torque is maximum, τ = pE. Its direction is such that the dipole rotates toward θ = 0°, where its dipole moment is parallel to the field and potential energy is minimum. Therefore option A gives the correct rotational tendency.

For a dipole in a uniform electric field, the positive and negative charges experience forces of equal magnitude in opposite directions, so their vector sum is zero. However, the forces act at two separated points rather than at the same point. Their separation forms a couple that produces torque τ = pE sinθ, which can rotate the dipole. Hence option A is correct. Zero net force describes translational equilibrium only; it does not guarantee zero torque or rotational equilibrium.

For a dipole in a uniform electric field, τ = pE sinθ, so the torque is zero at θ = 180° because sin180° = 0. However, this is an unstable equilibrium: after a small angular displacement, the torque acts in the direction that increases the displacement and turns the dipole toward θ = 0°, the stable orientation. Equivalently, U = −pE cosθ is maximum at 180°. Thus option A is correct; a restoring return would indicate stable, not unstable, equilibrium.

For a dipole in a uniform electric field, potential energy is U = −pE cos θ. In the stable equilibrium position, the dipole moment is parallel to the field, so θ = 0° and U = −pE, its minimum value. A small angular displacement therefore increases the energy and produces a restoring torque. Hence option A is correct; the antiparallel position has maximum energy, not minimum.

The potential energy of a dipole in a uniform electric field is U = −pE cos θ. In unstable equilibrium, the dipole moment is antiparallel to the field, so θ = 180° and U = +pE, the maximum possible value. A small displacement lowers the energy and causes the dipole to move farther from this orientation. Therefore option A is correct; the parallel orientation gives minimum energy.

The torque on an electric dipole in a uniform field is τ = pE sin θ. Thus its magnitude depends directly on the dipole moment p and the electric-field magnitude E, while also depending on the angle θ between them. Among the choices, only option A lists the two relevant electrical quantities. Mass, temperature, colour, density, and volume do not determine this electrostatic torque in the stated situation.

For a dipole in a uniform electric field, the torque magnitude is τ = pE sin θ. Keeping E and θ unchanged makes torque directly proportional to p. If the dipole moment changes from p to 2p, the new torque is τ′ = (2p)E sin θ = 2τ. Therefore option A, double, is correct; it is not half or four times, and it does not become zero unless the angle makes sin θ zero.