Final answer:
Option C: The torque on an electrical dipole in an electric field is 'pE sinθ', and its potential energy is '-pE cosθ', where 'p' is the dipole moment, 'E' is the electric field intensity, and 'θ' is the angle between the dipole axis and the electric field.
Step-by-step explanation:
The torque on a dipole in an electric field is given by the formula pE sinθ, where p is the dipole moment and E is the electric field intensity. In this case, the dipole has acquired a position such that the angle θ between its axis and the electric field is not 90°. Therefore, the torque on the dipole is pE sinθ.
The potential energy of a dipole in an electric field is given by the formula -pE cosθ, where p is the dipole moment and E is the electric field intensity. The negative sign indicates that the potential energy decreases as the angle θ increases.When an electrical dipole with dipole moment 'p' is placed in an electric field of intensity 'E', and the axis of the dipole makes an angle θ with the electric field, the dipole experiences torque and has potential energy dependent on the angle θ.
The torque (τ) on the dipole is given by the product of the dipole moment and the electric field intensity, multiplied by the sine of the angle between them, which can be expressed as τ = pE sinθ. The potential energy (U) of the dipole in the electric field is given by U = -pE cosθ, with the negative sign indicating that the potential energy is lowest when the dipole is aligned with the electric field. Since the potential energy is taken to be zero when the angle θ=90°, the correct answer is C. pE sinθ, -pE cos θ.