An electric dipole consists of two charges ±q separated by distance d; which pair of expressions correctly gives the dipole moment p and the potential energy in a uniform external field?

An electric dipole consists of two charges ±q separated by distance d; which pair of expressions correctly gives the dipole moment p and the potential energy in a uniform external field?

• A. p = q d; U = − p · E
• B. p = q / d; U = p · E
• C. p = 2 q d; U = − p × E
• D. p = q d; U = p × E

Answer: (C)

The dipole moment measures the strength and orientation of a two-charge system. It is defined as a vector p equal to q times the separation vector from the negative charge to the positive charge: p = q d_vec. For charges separated by a distance d, the magnitude is p = q d, and its direction is from the negative charge toward the positive one. In a uniform external electric field E, the potential energy of the dipole is given by U = - p · E. This scalar energy depends on how aligned the dipole moment is with the field: U = - p E cos(theta), where theta is the angle between p and E. The energy is lowest when p is aligned with E. It’s important to distinguish this from torque, which is given by tau = p × E. The cross product yields a vector perpendicular to the plane of p and E and represents torque, not energy (the energy uses the dot product). So the correct relationships are p = q d and U = - p · E. The pair that uses a cross product for energy or doubles the charge separation is not correct.

The dipole moment measures the strength and orientation of a two-charge system. It is defined as a vector p equal to q times the separation vector from the negative charge to the positive charge: p = q d_vec. For charges separated by a distance d, the magnitude is p = q d, and its direction is from the negative charge toward the positive one.

In a uniform external electric field E, the potential energy of the dipole is given by U = - p · E. This scalar energy depends on how aligned the dipole moment is with the field: U = - p E cos(theta), where theta is the angle between p and E. The energy is lowest when p is aligned with E.

It’s important to distinguish this from torque, which is given by tau = p × E. The cross product yields a vector perpendicular to the plane of p and E and represents torque, not energy (the energy uses the dot product).

So the correct relationships are p = q d and U = - p · E. The pair that uses a cross product for energy or doubles the charge separation is not correct.