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The electric dipole moment is a significant physical quantity in the study of electric fields. It is a vector quantity and is defined as the product of the charge magnitude and the separation distance between two charges. Here, the dipole moment is represented by the symbol \( \mathbf{p} \).
To calculate the dipole moment, the formula \( \mathbf{p} = q \cdot d \) is used, where \( q \) refers to the magnitude of one of the charges (since they are equal in magnitude), and \( d \) is the distance between them. In this scenario, both charges are numerically equal at \( 4.5 \times 10^{-9} \) C, separated by 3.1 mm or \( 3.1 \times 10^{-3} \) m. The resulting dipole moment is calculated to be \( 1.395 \times 10^{-11} \) C·m.
The direction of the dipole moment is crucial; it is defined to be from the negative to the positive charge, following a convention that makes it useful in vector calculations.

Torque, in the context of electric dipoles, can be thought of as the rotational effect exerted by an electric field on the dipole. It causes the dipole to experience a twisting force, aligning it with the direction of the field. Torque is given by the expression \( \tau = pE\sin\theta \). Here, \( \tau \) is the torque, \( p \) is the dipole moment, \( E \) is the electric field strength, and \( \theta \) is the angle between the electric field and the dipole moment vector.
The practical implication of this is that the dipole will reach a stable orientation when it aligns itself such that this torque is minimized or nullified. The maximum torque occurs when the angle is at 90 degrees (since \( \sin 90^\circ = 1 \)). In this specific exercise, the torque is provided as \( 7.2 \times 10^{-9} \) N·m. This torque tells us about the interaction strength between the dipole and the field.

A uniform electric field is characterized by having a constant magnitude and direction throughout a given space. This simplicity allows for straightforward calculations and predictions about the behavior of charges in the field.
For an electric dipole in such a field, the torque experienced depends directly on both the dipole moment and the field strength. This uniformity means the same electric influence is applied along the entire path of the dipole, ensuring calculable and consistent results.
When an electric dipole is placed in this field, it undergoes a torque that tries to align the dipole with the field direction, highlighting how external electric fields can influence charged systems through torque.

The angle between the dipole moment and the electric field is a crucial parameter when considering the torque. This angle, denoted as \( \theta \), determines how effectively the electric field exerts torque on the dipole.
The formula for torque incorporates this angle through the sine function: \( \tau = pE\sin\theta \). This implies that the torque is at its maximum when the angle is 90 degrees, and becomes zero when the dipole aligns perfectly with the field (0 or 180 degrees), meaning no rotational force is exerted.
In the exercise, the angle \( \theta = 36.9^\circ \) is a specific value that contributes to the calculation of the field strength when given the torque. By considering such angles, we better understand the dynamic equilibrium of dipoles in fields.