Orientation of electric dipole moment(p vector) in a uniform electric field

An electric dipole is a pair of electric charges of equal magnitude and opposite sign separated by a distance. When an electric dipole is placed in a uniform electric field, it experiences a torque. The orientation of the dipole moment vector (p) with respect to the electric field vector (E) determines the magnitude and direction of the torque.

1) Maximum torque:
The torque experienced by an electric dipole in a uniform electric field is maximum when the dipole moment vector is perpendicular to the electric field vector. This orientation is known as the anti-parallel orientation. In this orientation, the angle between p and E is 90 degrees. The torque is given by τ = pEsinθ, where θ is the angle between p and E. Since sin 90 = 1, the torque is maximum.

2) Minimum torque:
The torque experienced by an electric dipole in a uniform electric field is minimum when the dipole moment vector is parallel to the electric field vector. This orientation is known as the parallel orientation. In this orientation, the angle between p and E is 0 degrees. The torque is given by τ = pEsinθ, where θ is the angle between p and E. Since sin 0 = 0, the torque is minimum.

3) Half of the maximum torque:
The torque experienced by an electric dipole in a uniform electric field is half of the maximum torque when the dipole moment vector makes an angle of 45 degrees with the electric field vector. In this orientation, the angle between p and E is 45 degrees. The torque is given by τ = pEsinθ, where θ is the angle between p and E. Since sin 45 = 1/root 2, the torque is half of the maximum torque.

4) 1/root 2 times the maximum torque:
The torque experienced by an electric dipole in a uniform electric field is 1/root 2 times the maximum torque when the dipole moment vector makes an angle of 30 degrees with the electric field vector. In this orientation, the angle between p and E is 30 degrees. The torque is given by τ = pEsinθ, where θ is the angle between p and E. Since sin 30 = 1/2, the torque is 1/root 2 times the maximum torque.

5) 76.6% of the maximum torque:
The torque experienced by an electric dipole in a uniform electric field is 76.6% of the maximum torque when the dipole moment vector makes an angle of 60 degrees with the electric field vector. In this orientation, the angle between p and E is 60 degrees. The torque is given by τ = pEsinθ, where θ is the angle between p and E. Since sin 60 = root 3/2, the torque is 76.6% of the maximum torque.