Electrical potential energy

Almost every chemical reaction that occurs in your body is caused by electric forces. Almost all of the biochemistry is based on determining how these forces cause electrons to move between atoms, as well as the changes in structure or composition that occur when electrons move between atoms. However, the fundamental rules of electric forces are surprisingly simple: electrons repel other electrons, whereas protons and electrons attract one another. The electric force is the force that pushes two like charges apart or pulls two unlike charges together. Two different electric charges (such as a negatively charged electron and a positively charged proton) always want to join together, just like two magnets that snap together when the North end of one magnet is pointed towards the South end of the other. As the distance between them grows, the size of this attraction shrinks. Electric potential energy is a potential energy (measured in joules) resulting from conservative Coulomb forces and associated with the configuration of a specific set of point charges within a defined system. An object can have electric potential energy due to two factors: its own electric charge and its position in relation to other electrically charged objects. The term “electrical potential energy” refers to potential energy in systems with time-varying electric fields, whereas “electrostatic potential energy” refers to potential energy in systems with time-invariant electric fields. Electric potential energy is the energy required to move a charge against an electric field. More energy is required to move a charge further in the electric field, but even more, energy is required to move it through a stronger electric field.

Overview

The electrical potential energy of a system is defined as the effort necessary to assemble a system of point charges by bringing them near together, as in the system from an infinite distance. Alternatively, the entire work performed by an external agent in moving a charge or system of charges from infinity to the current configuration without acceleration is defined as the charge or system of charges’ electric potential energy. The electric potential energy of an object is determined by two factors: the object’s own charge and the object’s relative position in relation to other electrically charged objects. The amount of work required to move an object from one location to another in the presence of an electric field determines the magnitude of the electric potential. An item gains energy when it moves against an electric field, which is referred to as electric potential energy. Divide the potential energy by the quantity of charge to get the electric potential for any charge. The entire work done by an external agent in moving a charge or system of charges from infinity to the current configuration without acceleration is defined as the electric charge’s or system of charges’ potential energy. The magnitude of electric potential energy is a scalar quantity with no direction. It is denoted by the letters V and is measured in Joules. Its dimensional formula is ML²T^-3A^-1.

When a positive charge moves against an electric field, its potential energy grows, and when it moves with the electric field, it reduces; when a negative charge moves with the electric field, its potential energy drops. Unless the unit charge passes through a changing magnetic field, its potential is independent of the path followed at any given place. Electric potential is a valuable notion for understanding electrical phenomena, but only potential energy differences are quantifiable. If an electric field is defined as the force per unit charge, an electric potential can be conceived of as the potential energy per unit charge. As a result, the effort required to carry a unit charge from one location to another (for example, within an electric circuit) is equal to the potential energy difference between each point. The International System of Units (SI) expresses electric potential in joules per coulomb (volts), and potential energy differences are measured with a voltmeter.

Electric Potential Formula:

The potential energy of a charge in an electric field is measured by the work done in moving the charge from infinity to that point against the electric field. If two charges, q1 and q2, are separated by a distance d, the system’s electric potential energy is;

U = [1/(4πε_o)] × [q₁q₂/d]

When two like charges (two protons or two electrons) are brought together, the system’s potential energy increases. When two opposite charges, such as a proton and an electron, are brought together, the system’s electric potential energy decreases.

Electric Potential Derivation

Consider the charge q1. Assume they are separated by a distance ‘r’. The charge’s total electric potential is defined as the total work done by an external force in bringing the charge from infinity to the given point.

-∫ (r_a→r_b) F.dr = – (U_a – U_b)

We can see that the point rb is at infinity, and the point ra is r.

-∫ (r →∞) F.dr = – (U_r – U_∞)

-∫ (r →∞) F.dr = -U_R

⇒ -∫ (r →∞) [-kqq_o]/r² dr = -U_R

Or, -k × qq_o × [1/r] = U_R

Therefore, U_R = -kqq_o/r

Zero of Potential

An arbitrary value is a point at which an object has no potential. This is similar to how we frequently measure gravitational potential energy relative to the ground, despite the fact that if the ground were moved, a ball would continue to fall until it reached the centre of the Earth. For simplicity, the zero of potential is frequently placed at a distance of zero between two charges. However, in more advanced physics, we tend to put zero at infinity for point charges, which means that two charges separated by an infinite distance will have a potential of zero.

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FAQs

What is the difference in electric potential?

The potential (E) between two points in an electrical circuit is defined as the amount of work (W) done by an external agent in moving a unit charge (Q) from one point to another. Mathematically, we can state: W/Q = E

What is the definition of Electric Potential Energy?

Electric potential energy is defined as the total potential energy that a unit charge will have if it is located anywhere in space.

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