Dipole in a Uniform External Field

The electric force on a charge is F = qE. For the positive charge, q > 0, so the force has the same direction as the electric field. Therefore option A is correct. The negative charge of the same dipole experiences a force opposite to the field, which is why the two forces can produce torque. The force is not always zero; only special net-force conditions can make the resultant zero.

The governing relation is F = qE. For a negative charge, q is negative, so the force vector is opposite to the electric-field vector. Therefore, the negative charge of the dipole experiences force opposite to the field, making option A correct. The positive charge experiences force along the field; hence the two dipole forces are equal and opposite in a uniform field. Options C and D ignore charge sign and field direction.

The torque on an electric dipole in a uniform field is τ = pE sin θ. Its action tends to reduce the angle θ between the dipole moment p and the electric field E, bringing them into the same direction. The aligned position is stable because the potential energy U = −pE is minimum there. Hence option A is correct; perpendicular orientation gives maximum torque, not permanent alignment.

In a uniform electric field, the charges +q and −q of a dipole experience equal forces in opposite directions. Their vector sum is zero, so the net translational force is zero, but because the forces act along different lines, they form a couple and produce torque τ = pE sinθ. The torque tends to align p with E. Therefore option A is correct.

The governing idea is that a dipole in a uniform electric field experiences equal and opposite forces on its two charges. The positive charge is pushed along the field and the negative charge against it. Therefore, their vector sum is zero, although the separated forces can produce a torque. Hence option A is correct; the other choices confuse net force with torque or assume an unsupported direction.

For a dipole in a uniform electric field, the torque magnitude is given by τ = pE sin θ, where θ is the angle between dipole moment p and field E. Since sin 0° and sin 180° are both zero, torque vanishes when the two vectors are parallel or antiparallel. Thus option A is correct. At 90°, torque is maximum, so option B is the opposite case.

The torque on an electric dipole is τ = pE sin θ. For fixed dipole moment p and field E, the largest possible value of sin θ is 1, which occurs at θ = 90°. Therefore, the dipole moment must be perpendicular to the electric field, giving τmax = pE. Option A is correct. Parallel alignment gives zero torque, while zero field or zero charge also gives zero torque, not a maximum.

A dipole in a uniform electric field experiences zero net force but generally experiences torque τ = pE sin θ. This torque rotates the dipole so that its dipole moment p moves toward the direction of E. The parallel orientation is stable because the potential energy U = −pE cos θ is minimum there. Thus option A is correct; the other choices do not describe the electric torque.

The potential energy of a dipole in a uniform electric field is U = −pE cos θ. At θ = 0°, the dipole moment is parallel to the field and U is minimum, so a small angular displacement produces a restoring torque; this is stable equilibrium. At θ = 180°, energy is maximum and equilibrium is unstable. Therefore option A is correct, while perpendicular alignment is not an equilibrium orientation for a nonzero field.

For a dipole in a uniform field, U = −pE cos θ. When θ = 180°, the dipole moment is antiparallel to the field and the potential energy is maximum, U = +pE. A small displacement then produces a torque that moves the dipole farther from this orientation, so it is unstable equilibrium. Hence option A is correct; parallel alignment has minimum energy and is stable.

The potential energy of a dipole in a uniform electric field is U = −p·E = −pE cosθ. When the dipole moment and field are parallel, θ = 0°, so U = −pE, the minimum possible value for fixed p and E. Hence option A is correct. The antiparallel arrangement gives maximum energy +pE, while perpendicular orientation gives zero energy.

For a dipole in a uniform electric field, U = −pE cosθ. In the opposite, or antiparallel, orientation, θ = 180° and cosθ = −1, giving U = +pE, the maximum value for fixed p and E. Therefore option A is correct. This is an unstable equilibrium because a small rotation produces torque that tends to turn the dipole toward the field direction.

In a uniform electric field, the positive charge experiences force +qE and the negative charge experiences force −qE. These forces have equal magnitudes and opposite directions, so their vector sum is zero: F_net = qE − qE = 0. Therefore option A is correct. A torque can still act when the dipole is tilted, so zero net force does not mean zero rotational effect.

The torque on a dipole in a uniform field is τ = pE sin θ, where θ is the angle between the dipole moment and the field. For parallel alignment, θ = 0°, so sin θ = 0 and τ = 0; the antiparallel case also gives zero. Among the choices, option A is correct. Perpendicular alignment gives maximum torque, not zero torque.

The torque magnitude on a dipole is τ = pE sin θ. For fixed dipole moment p and field E, sin θ reaches its maximum value, 1, when θ = 90°. Therefore τ_max = pE and the dipole moment is perpendicular to the field, making option A correct. Parallel alignment gives zero torque, while zero charge or zero separation gives no effective dipole moment.

A dipole in a uniform electric field has zero net translational force, but it experiences torque τ = pE sin θ when its dipole moment is not aligned with the field. This torque reduces the angle θ and tends to rotate p into the field direction, the stable orientation. Hence option A is correct. The dipole does not lose charge or automatically vanish.

Gauss’s law depends only on the net charge enclosed by a closed surface. An external charge can certainly produce an electric field on the surface, so option B is false. However, its field lines that enter the surface must leave it elsewhere; inward and outward contributions cancel in the closed integral. Thus its net flux contribution is zero.

In a non-uniform electric field, the field magnitude can differ at the positions of the positive and negative charges. The forces qE on the two charges may therefore have unequal magnitudes, so they do not completely cancel and a net force can act on the dipole. Option A is correct. In a uniform field the net force is zero, though torque may act; the dipole’s charges and moment do not disappear merely because the field is non-uniform.

The torque on an electric dipole in a uniform field is τ = pE sin θ. If E and θ remain constant, torque is directly proportional to the dipole moment p. Thus, increasing p increases τ in the same ratio; for example, doubling p doubles the torque. Option A is correct. The torque would be zero only when θ is 0° or 180°, not merely because p changes.

The magnitude of torque on a dipole is τ = pE sin θ. Here p and θ are unchanged, so τ is directly proportional to E. Replacing E by 2E gives τ′ = p(2E)sin θ = 2τ. Therefore the torque doubles and option A is correct. It becomes zero only for a parallel or antiparallel orientation, and it becomes four times only if both p and E were doubled.

The torque on an electric dipole in a uniform field is τ = pE sinθ, where θ is the angle between the dipole moment and the electric field. For θ = 90°, sin90° = 1, so τ = pE, its greatest possible value for fixed p and E. Therefore option A is correct. Torque is zero when the dipole is parallel or antiparallel to the field, because sin0° and sin180° are both zero; it is not half at ninety degrees.

The torque on a dipole in a uniform electric field is τ = pE sinθ. When the dipole moment is parallel to the field, θ = 0°, and sin0° = 0; hence τ = 0. Physically, the equal and opposite forces on the two charges act along the same line, so they do not form a turning couple. Option A is correct. The charges do not disappear, the field unit is unchanged, and dipole torque does not depend on an area becoming zero.

The torque on an electric dipole in a uniform field is τ = pE sin θ, where θ is the angle between dipole moment p and field E. Its maximum value occurs when sin θ = 1, which means θ = 90°. Thus the dipole moment must be perpendicular to the field. For parallel or antiparallel alignment, sin θ is zero and the torque vanishes.

For a dipole in a uniform electric field, torque is τ = pE sin θ. It becomes zero when sin θ = 0, which occurs at θ = 0° or 180°. These are the parallel and antiparallel orientations of the dipole moment with respect to the field. At 90°, torque is maximum, so the perpendicular option is not correct; field strength alone does not make torque zero.