Dipole in a Uniform External Field

The torque magnitude on a dipole is τ = pE sin θ. With p and θ fixed, torque is directly proportional to the electric-field magnitude E. Replacing E by 2E gives τ′ = p(2E) sin θ = 2τ, so the torque doubles. Option A is correct. It would remain the same only if the field were unchanged, and it would be zero only for a parallel or antiparallel orientation.

The torque on a dipole is τ = pE sin θ, where θ is the angle between p and E. When the dipole moment lies along the field line, θ = 0°; if it is opposite to the field, θ = 180°. In either case sin θ = 0, so there is no rotational tendency. Option A describes the parallel case. At 90°, torque is maximum, not zero.

The correct answer is A. A dipole contains charges +q and −q, and each experiences a force F = qE at its location. In a uniform field, the field values at both charges are equal, so the forces cancel and only a torque may remain. In a non-uniform field, the magnitudes of the two forces can differ, producing a resultant force as well as torque. Hence torque is not the only possible effect.

The correct answer is A. A dipole has charges +q and −q separated by a small distance. In a uniform electric field, both charges experience the same field magnitude, so the force magnitudes are qE and qE, but their directions are opposite because the charges have opposite signs. Their vector sum is therefore zero. The forces can still form a couple and produce torque when the dipole is not aligned with the field.

The correct answer is A. The torque on an electric dipole in a uniform field is τ = pE sinθ, where θ is the angle between p and E. This torque acts so that the dipole moment rotates toward the field direction, reducing θ and lowering the potential energy U = −p·E. Parallel alignment is stable, whereas exact anti-parallel alignment is an unstable equilibrium.

The potential energy of a dipole in a uniform electric field is U = −pE cos θ. For the parallel orientation, θ = 0° and U = −pE, the minimum value. For the antiparallel orientation, θ = 180° and U = +pE, the maximum value. The increase is ΔU = 2pE, so an external agent must supply positive work if the rotation is slow and controlled. Therefore option A is correct.

A dipole in a uniform electric field has potential energy U = −pE cos θ. The torque tends to rotate the dipole so that its moment aligns with the field, reducing θ toward zero. This changes the system toward the stable minimum-energy state U = −pE. Thus a freely released dipole tends to decrease its potential energy, making option A correct. It does not necessarily make the energy zero or move independently of energy.

A dipole contains charges +q and −q separated by a small distance. In a uniform field, the electric field has the same magnitude and direction at both charge positions. The forces are F₊ = qE and F₋ = −qE, so their vector sum is zero. A torque may still act, but the net translational force is zero; the other options contradict the definition of a dipole.

The potential energy of an electric dipole in a uniform field is U = −pE cos θ. This energy is minimum when θ = 0°, meaning the dipole moment is along the field. The torque also tends to rotate the dipole toward this orientation. The antiparallel position has maximum energy and is unstable, while a perpendicular position is not the minimum-energy equilibrium.

For a dipole in a uniform electric field, τ = pE sin θ. In the antiparallel orientation θ = 180°, so torque is momentarily zero and the position is an equilibrium. However, its potential energy U = −pE cos θ is maximum there. A small angular displacement produces a torque that increases the displacement, so the equilibrium is unstable, not stable or torque-maximal.

A dipole consists of equal and opposite charges separated by a finite distance. In a uniform external electric field, the two charges experience equal forces in opposite directions. The net translational force is therefore zero, but because the forces act at different points, they form a couple and produce torque, given by τ = pE sin θ. Thus option A is correct; the other statements contradict the definition of a dipole or of an electric field.

The torque on an electric dipole in a uniform electric field is τ = pE sin θ, where p is the dipole moment and θ is the angle between p and E. For a perpendicular position, θ = 90°, so sin θ = 1 and τ = pE. If E is unchanged and p is replaced by 2p, the new torque is τ′ = 2pE = 2τ. Therefore, option A is correct.

For a dipole in a uniform electric field, the torque is τ = pE sin θ. In the perpendicular position, θ = 90°, so τ = pE. Since p remains unchanged while E becomes 2E, the new torque is τ′ = p(2E) = 2pE = 2τ. Hence the torque doubles. It does not become zero because the angle is still 90°, and it is not inversely proportional to the field.

The torque on a dipole in a uniform electric field is τ = pE sin θ. With p and E unchanged, the comparison depends only on the sine of the angle. Initially τ₁ = pE sin 60° = (√3/2)pE, whereas finally τ₂ = pE sin 30° = (1/2)pE. Since 1/2 is smaller than √3/2, the torque decreases. Therefore option A is correct.

The torque on an electric dipole in a uniform external field is given by τ = pE sin θ, where p is dipole moment, E is field magnitude, and θ is the angle between them. If p becomes 2p and E becomes 2E while θ remains unchanged, the new torque is (2p)(2E)sin θ = 4τ. Therefore, option A is correct. Options B and C account for only one change, while D ignores the proportional dependence on both quantities.

For a dipole in a uniform electric field, torque is τ = pE sin θ. The angle remains the same, so sin θ does not change. After the stated changes, p' = 2p and E' = E/2; hence τ' = (2p)(E/2)sin θ = pE sin θ = τ. Thus the torque remains unchanged, making option A correct. The other choices result from changing only one factor or multiplying the factors incorrectly.

For a dipole in a uniform electric field, the forces on +q and −q have equal magnitudes and opposite directions, so their vector sum is zero. The torque magnitude is τ = pE sin θ. At θ = 90°, sin θ = 1, giving the maximum torque τ_max = pE. Therefore option A is correct. A zero torque occurs at 0° or 180°, not at 90°, and “negative net force” is not a valid vector description here.

The torque on a dipole is τ = pE sin θ. At θ = 0°, the torque is zero, so the aligned position is an equilibrium position. Stability requires examining a small angular displacement: when θ becomes slightly positive, the torque acts in the direction that reduces θ and returns the dipole toward alignment. Equivalently, the potential energy U = −pE cos θ has a minimum at θ = 0°. Hence option A is correct; the other statements contradict the dipole model.

For a dipole, τ = pE sin θ. At θ = 180°, the instantaneous torque is zero, so this is an equilibrium orientation. However, after a small displacement from 180°, the torque acts so that the dipole rotates toward θ = 90° and then toward θ = 0°, rather than returning to 180°. The potential energy U = −pE cos θ is maximum at 180°, confirming unstable equilibrium. Therefore option A is correct.

The torque on an electric dipole in a uniform field is τ = pE sin θ. Since θ is unchanged, sin θ is unchanged. The new torque is τ′ = (2p)(3E)sin θ = 6pE sin θ = 6τ. Thus the torque becomes six times its original value. The factors should be multiplied, not added; the unchanged angle does not introduce any extra factor.

For a dipole in a uniform electric field, τ = pE sin θ. With the angle fixed, the torque changes in proportion to pE. The change factor is (p′/p)(E′/E) = 3 × 1/2 = 3/2. Therefore τ′ = 1.5τ, or one and a half times the original torque. The field becoming half does not cancel the tripling completely; their factors must be multiplied.

The torque on a dipole in a uniform electric field is τ = pE sin θ. At θ = 60°, sin 60° = √3/2, which is nonzero; therefore the two equal and opposite forces form a couple that tends to rotate the dipole. The net force on the dipole is actually zero in a uniform field, so option B is not the reason. Torque vanishes only at 0° or 180°.

A polar molecule has a permanent electric dipole moment p because its centres of positive and negative charge are separated. In a uniform electric field E, the opposite charges experience equal and opposite forces. Their net force is zero, but the forces form a couple with torque τ = pE sin θ. This torque tends to reduce θ, so the dipole aligns with the field. The other options incorrectly deny charge or torque.

In a uniform electric field, each charge of a dipole experiences a force: the positive charge is pushed along E and the negative charge is pushed opposite to E. Since the charges have equal magnitude and the field is uniform, the two forces have equal magnitudes and opposite directions. Their vector sum is therefore zero, although each individual force can be nonzero. This pair of forces may still produce a torque.

For a dipole in a uniform electric field, the forces on its two charges are equal and opposite, so the net translational force is zero. The torque is τ = pE sin θ, where θ is the angle between the dipole moment and the field. With the dipole perpendicular to the field, θ = 90° and sin θ = 1; hence τ = pE, its maximum value. Therefore option A correctly combines both results.