1. What orientation of an electric dipole in a uniform electric field has the greatest electric potential energy? What orientation has the least? (Let the system comprise both the electric dipole and the sources of the uniform electric field.) -

An electric dipole consists of two equal and opposite charges separated by a distance. When placed in a uniform electric field, the orientation of the dipole relative to the field affects its electric potential energy. 1. **Greatest Electric Potential Energy**: The electric potential energy \( U \) of an electric dipole in a uniform electric field \( \mathbf{E} \) is given by the equation: \[ U = -\mathbf{p} \cdot \mathbf{E} = -pE \cos(\theta) \] where: - \( \mathbf{p} \) is the dipole moment, - \( \theta \) is the angle between the dipole moment and the electric field, - \( E \) is the magnitude of the electric field. The potential energy is greatest when \( \cos(\theta) \) is at its maximum value, which occurs when \( \theta = 180^\circ \) (the dipole is aligned opposite to the field). In this orientation, the potential energy is at its maximum value (least negative). 2. **Least Electric Potential Energy**: The electric potential energy is least (most negative) when \( \cos(\theta) \) is at its minimum value, which occurs when \( \theta = 0^\circ \) (the dipole is aligned in the same direction as the electric field). In this orientation, the potential energy is at its minimum value. In summary: - **Greatest Electric Potential Energy**: Dipole aligned opposite to the field (\( \theta = 180^\circ \)). - **Least Electric Potential Energy**: Dipole aligned in the same direction as the field (\( \theta = 0^\circ \)).