Question

An electric dipole consists of two equal and opposite charges situated a very small distance from each other. When the dipole is placed in a uniform electric field, which of the following statements is true? a) The dipole will not experience any net force from the electric field; since the charges are equal and have opposite signs, the individual effects will cancel out. b) There will be no net force and no net torque acting on the dipole. c) There will be a net force but no net torque acting on the dipole. d) There will be no net force, but there will (in general) be a net torque acting on dipole.

Short answer

(a) There will always be a net force and torque acting on the dipole; (b) There will never be a net force or torque acting on the dipole; (c) There will always be a net force and sometimes a net torque acting on the dipole; (d) There will be no net force, but there will (in general) be a net torque acting on the dipole. Answer: (d) There will be no net force, but there will (in general) be a net torque acting on the dipole.

Step-by-step solution

Understanding Electric Dipole

An electric dipole consists of two equal and opposite charges placed at a very small distance from each other. In a uniform electric field, each charge will experience a force proportional to the product of the charge and the electric field. The force on the positive charge will act in the direction of the field, while the force on the negative charge will act in the opposite direction.

Net Force Acting on the Dipole

Since the charges are equal and opposite, and the electric field is uniform, the magnitude of the forces acting on each charge due to the electric field will be the same. However, these forces will be acting in opposite directions, thus they will cancel each other out and the net force on the dipole will be zero.

Net Torque Acting on the Dipole

To determine the net torque acting on the dipole, we need to calculate the torque due to the forces acting on each charge. Torque (\tau) is the cross product of the position vector (r) and the force vector (F): \tau = r \times F. Since the forces are acting at opposite ends of the dipole and in opposite directions, they will produce a torque in the same direction, causing the dipole to rotate. In general, if the dipole is not aligned with the electric field, there will be a net torque acting on it. However, when the dipole is aligned with (or in the opposite direction of) the electric field, the net torque will be zero. Based on the analysis of net force and net torque, the correct answer is: d) There will be no net force, but there will (in general) be a net torque acting on the dipole.

Key concepts

Net Force

In the context of electric dipoles, understanding the concept of net force is crucial. An electric dipole consists of two charges that are equal in magnitude but opposite in sign, separated by a small distance. When this dipole is placed within a uniform electric field, each charge encounters a force. For the positive charge, this force is in the direction of the electric field, while for the negative charge, the force is in the opposite direction.
Since these are equal forces and act in opposite directions, they cancel each other out, resulting in a net force of zero. In simple terms, it's like pulling a rope equally in both directions—nothing moves. This means that any potential movement due to force is balanced, keeping the dipole stationary in terms of force. Thus, a uniform electric field does not alter the position of the dipole since the net force remains zero.

Net Torque

While the net force on an electric dipole in a uniform electric field is zero, that doesn't mean the dipole remains unaffected. Torque comes into play here and is a different story. Torque essentially refers to the rotational effect produced by forces on an object. For a dipole in an electric field, the torque measures how much a force causes the dipole to rotate or twist around a point.
The concept can be grasped by considering how the forces exerted on both charges at either end of the dipole operate. These forces, though equal and opposite, act at different points of the dipole, creating a couple. The effect is a turning or rotational force, known as torque. This is why a dipole that is not aligned with the electric field will experience this rotational effect until it aligns itself parallel or anti-parallel to the field. Remember, the net torque is non-zero when the dipole is misaligned with the field, driving it to achieve alignment through rotation.

Uniform Electric Field

A uniform electric field is a region where every point has the same electric field strength and direction. Imagine a field with identical electric lines running parallel and spaced equally—it represents uniformity in electrical influence.
Understanding its impact on an electric dipole involves visualizing how this consistent field affects charges. While it impacts each charge of a dipole equally in magnitude, the direction of forces varies due to the opposite nature of charges in a dipole. Hence, despite significant individual forces, the overall movement caused by force is neutralized. However, this uniform field's symmetry leads to a balanced distribution of forces, crucial in understanding dipole behavior and its tendency to experience torque.

Dipole Alignment

Dipole alignment occurs when an electric dipole experiences forces and torques in an electric field that tend to make it line up with the field lines. This behavior stems from the torque exerted on the dipole when not about the aligned orientation, attempting to rotate it into or opposite to the direction of the field.
The field exerts a torque pushing the dipole into alignment because it is energetically favorable for the dipole to lay parallel to the field lines—like a compass needle aligning with Earth's magnetic poles. This alignment minimizes the system's potential energy, where no torque acts on the dipole once it is perfectly aligned either parallel or anti-parallel with the field. Therefore, understanding dipole alignment provides insights into the dynamic equilibrium and stability tendencies in electric fields.