For a dipole in a uniform external field, if θ = 180 degrees (dipole moment opposite to E), the potential energy is:

For a dipole in a uniform external field, if θ = 180 degrees (dipole moment opposite to E), the potential energy is:

• A. − p E
• B. + p E
• C. 0
• D. Undefined

Answer: (B)

The test is about how the dipole’s potential energy in a uniform electric field depends on orientation. The energy is given by U = - p · E = - p E cos θ, where θ is the angle between the dipole moment p (from negative to positive charge) and the field E. If θ is 180°, the dipole is opposite to the field, so cos(180°) = -1. Plugging in gives U = - p E (-1) = + p E. So the energy is positive and equal to pE. This orientation corresponds to the maximum potential energy for a dipole in a uniform field (the dipole would energetically prefer to flip to align with the field, where the energy is -pE). At this exact angle, the torque, which is τ = p × E with magnitude pE sin θ, is zero because sin(180°) = 0, meaning the dipole is momentarily stationary but at a maximum in energy.

The test is about how the dipole’s potential energy in a uniform electric field depends on orientation. The energy is given by U = - p · E = - p E cos θ, where θ is the angle between the dipole moment p (from negative to positive charge) and the field E.

If θ is 180°, the dipole is opposite to the field, so cos(180°) = -1. Plugging in gives U = - p E (-1) = + p E. So the energy is positive and equal to pE. This orientation corresponds to the maximum potential energy for a dipole in a uniform field (the dipole would energetically prefer to flip to align with the field, where the energy is -pE). At this exact angle, the torque, which is τ = p × E with magnitude pE sin θ, is zero because sin(180°) = 0, meaning the dipole is momentarily stationary but at a maximum in energy.