Question

Consider an electric dipole in a uniform electric field. In which orientation does the dipole-field system have the greatest potential energy? when the dipole moment and the electric field are parallel when the dipole moment and the electric field are antiparallel when the dipole moment makes the 60∘ angle with the electric field when the dipole moment and the electric field are perpendicular

Answer 1

The electric dipole has the greatest potential energy in a uniform electric field when the electric dipole moment and the electric field are antiparallel.

Step-by-step explanation:

The potential energy of an electric dipole in a uniform electric field depends on its orientation. The potential energy (U) of a dipole in an electric field (E) is given by the formula U = -p·E, where p is the electric dipole moment and · indicates the dot product, which takes into account the angle between the dipole moment and the electric field vectors.

The potential energy is greatest when the dipole moment is antiparallel to the electric field because the negative sign in the formula indicates that U is maximum when the cosine of the angle (which is part of the dot product calculation) is -1, which happens when the angle between p and E is 180 degrees. Conversely, the potential energy is lowest (most negative) when the dipole moment is parallel to the electric field as the cosine of 0 degrees is 1, which due to the negative sign in the formula results in the minimum potential energy.

Orientations at any other angles, such as 60 degrees or when the dipole is perpendicular to the field, will have potential energies between these two extremes.

Answer 2

Answer: when the dipole moment and electric field are parallel

Explanation: The formulae that relates the potential energy of a dipole, dipole moment and strength of electric field is given as

u = p * E cosθ

Where, u= dipole potential energy, p = dipole moment, E = strength of electric field.

The expression is at maximum when θ = 0 (cos 0° = 1)

Hence the function for potential energy will be greatest when θ = 0° which implies that the dipole moment and strength of electric field are parallel to each other.