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The electrostatic potential energy of a system of two point charges is a system that involves at least two charges. We know that when there is a charge q, the electric field is at a distance of r. The simple formula of Kq/r2 calculates this. If the charge is positive, then the field is away from the charge and when it is negative, it is towards the charge. The potential energy of charge q at the distance of r has to be calculated.
Electrostatic Potential Energy
The energy gained by a particular charge situated at infinity when it moves along the distance r is known as the electrostatic potential energy. However, the electrostatic potential energy of a single charge q is not defined, so it becomes equal to zero. This is measured by dividing Joules by coulomb and is denoted by a capital J.
The electrostatic potential energy is defined as Uf – Ui= -W conservative Forces. This means the negative of the work done by conservative forces is called the electrostatic potential of a charge. The electrostatic potential energy of a system of two point charges is considered because they always come in a configuration of two charges. Namely, the charges q1 and q2. There is no such defined scope of the potential of a single charge. The difference or the change in the potential energy is the only thing that can be calculated.
Electrostatic Potential Difference of a System of Two Charges
The difference between the Electrostatic Potential Energy at two points is calculated by the work that amounts to the movement of the charge from point ‘A’ at infinity to point ‘B.’ If the distance between these two points at infinity is assumed to be dx, we can calculate the work done to move it from point ‘A’ to point ‘B.’
∫ 𝑑𝑤 = ∫ ( 𝑘Q/ x2 ) dx
As we know that the work done is calculated as W = KQ [( 1/r1 ) – (1/r2)]
So , VAB = VA – VB = KQ [( 1/r1 ) – (1/rf2)]
Electrostatic Potential of a Dipole in an Electric Field
There are several things in which a pair of negative and positive charges are observed. These charges together form an electric dipole. To determine a dipole’s electric field, we need to consider two charges +q and -q that are equally distanced from each other. The electric field of these two points lies at point P and has a distance of r from each charge. In such a scenario, the magnitude of the electric field will be:
E=k q/r 2
The formula for the dipole in an electric field is the electrostatic potential of charges +q and -q. the formula used got the following is as follows
Cause by ‘-q’
V1 = q/(40( r+acosϴ))
Caused by ‘+q’
V2 = q/(40( r-acosϴ))
Electrostatic Potential Energy in terms of Dipole Moment
A dipole is when there are two opposite charges present and the mathematical equation of the dipole moment is formulated by multiplying the difference between the two charges and the magnitude of these charges.
Conclusion
The energy gained by a charge when it travels from one point at infinity to another is measured in terms of work. This phenomenon is called electrostatic energy. The charge causes this that the object may have its electric charge that may be positive or negative and the relative position of the charge. This makes it a vector quantity. It is expressed in joules. The forces that operate on it are called the Coulomb conservative forces and the relative position has to be calculated keeping in mind the configuration of the nearest charge.
