MHTCET 11 May 2024 Shift 2 Paper

Concept:For an electric dipole in a uniform electric field, potential energy depends on the angle between the dipole moment and the field, and it is minimum when the dipole is aligned with the field.Explanation:The potential energy $U$ of an electric dipole in an external electric field $E$ is given by:$$U = -\mathbf{p} \cdot \mathbf{E} = -pE\cos\theta$$Here, $\mathbf{p}$ is the dipole moment, $E$ is the field magnitude, and $\theta$ is the angle between $\mathbf{p}$ and $\mathbf{E}$.For minimum potential energy, $U$ must be as negative as possible.This requires $\cos\theta$ to be maximum, and the maximum value of $\cos\theta$ is $1$.So, $\cos\theta = 1$, which gives $\theta = 0^\circ$.Thus, the dipole must be parallel to the electric field, meaning it subtends an angle of zero with the field direction.Answer:The electric dipole has minimum potential energy when it subtends zero angle with the direction of the field.Therefore, the correct option is D: zero with the direction of field.