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An electric dipole consists of two equal and opposite charges separated by a distance. The electric dipole moment, denoted as \( p \), represents the strength and orientation of this setup. It is crucial for understanding physical interactions in electric fields.
To compute the dipole moment, we use the equation \( p = q \cdot d \), where:

• \( q \) is the magnitude of the charge.
• \( d \) is the distance between the charges.

For example, if the charges are \( 1.50 \mathrm{nC} \) or \( 1.50 \times 10^{-9} \text{ C} \), and they're separated by \( 6.20 \mu \mathrm{m} \) or \( 6.20 \times 10^{-6} \text{ m} \), the dipole moment becomes: \[ p = 1.50 \times 10^{-9} \text{ C} \times 6.20 \times 10^{-6} \text{ m} = 9.30 \times 10^{-15} \text{ C}\cdot\text{m} \]This value provides insight into how strongly the dipole can influence or be influenced by external electric fields.

The potential energy of a dipole in an electric field depends on its orientation relative to the field. When a dipole changes orientation, there is a difference in potential energy, which is vital for understanding how dipoles behave in fields.
To find the energy difference, we consider the formula for potential energy, \( U = -pE \cos(\theta) \). Here:

• \( p \) is the dipole moment.
• \( E \) is the electric field strength.
• \( \theta \) is the angle between \( p \) and \( E \).

For parallel orientation, \( \theta = 0^\circ \), so \( \cos(0^\circ) = 1 \). For antiparallel, \( \theta = 180^\circ \), so \( \cos(180^\circ) = -1 \). Therefore, the potential energy difference, \( \Delta U \), is:\[ \Delta U = -pE(\cos(0) - \cos(180)) = -pE(1 - (-1)) = -2pE \] Using the given \( p = 9.30 \times 10^{-15} \text{ C}\cdot\text{m} \) and \( E = 1100 \text{ N/C} \), we find:\[ \Delta U = -2 \times 9.30 \times 10^{-15} \text{ C}\cdot\text{m} \times 1100 \text{ N/C} = -2.046 \times 10^{-11} \text{ J} \]This energy change highlights the potential for work when orienting dipoles in fields.

Electric field strength, represented by \( E \), measures how strong an electric field is at a given point. This is crucial for predicting how charges within the field will react.
It's defined mathematically as \( E = F/q \), where \( F \) is the force experienced by a positive test charge \( q \). The units for electric field strength are Newtons per Coulomb (N/C).
A stronger field means that a test charge would experience a greater force. For the dipole considered here, the electric field strength is \( 1100 \text{ N/C} \), indicating a robust field that will significantly influence the dipole’s orientation.
Understanding the electric field is vital because it determines how much work is performed when a dipole aligns or realigns in the field. It also influences the calculation of potential energy differences as shown in the previous section. This foundational concept is key to mastering topics in electromagnetism.