A figure is a pictorial representation of numerical or mathematical data. Figure 1 shows three points A, B, and C. Point C has an electric potential of 50 V while point A has a potential of 30V and point B has a potential of 0 V.
The electric potential at the point indicated with the dot in the figure is found by calculating 50*30 + 0 = 900 V.
In this math problem, the word “potential” is defined as voltage multiplied by current. In terms of the electric potential, when there is no current, there is no voltage and the potential cannot be measured. It is required to know the current. For example, in a battery with a dielectric reference capacitor, one must know the battery’s chemical reactions to “calculate” the potential of a point on its plates.
The electric potential at any point is a vector quantity for which both magnitude (“V”) and direction are required. The electric potential can be positive or negative depending on whether or not an electrical current is flowing in that direction. If there is an electrical current in that direction then the vector has a positive magnitude (“V”). If there is no current then it has a negative value (“V”).
The electric potential at a point is independent of the shape, size, distance, or other properties of the point. In the figure on the left, point C has an electric potential of 50 V at a distance “d” from point B. However, if we add a new point to that figure then move it closer to B and measure its electric potential – that resulting vector will not be 50 V but will differ from that value by some amount depending on all of those same properties.
The concept of electric potential is fundamental in physics and engineering. A complex macroscopic manifestation of electric potential is voltage. In the same way, an object’s gravitational “potential” (as a function of position) can be calculated from the object’s overall mass and its distribution of mass.
Electric potential is a vector quantity, with both magnitude (“V”) and direction . The symbol for electric potential is formula_1:
where the Greek letter phi indicates electrical potential, “V” represents voltage in units of joules per coulomb (which is also a unit), and “q” represents a charge in units of coulombs (of electron charge).
The electric potential of a point is the product of electric charges on all other points on a closed surface surrounding the point. It is defined as the work done in moving electric charge from one point to another.
If there is an electrical current in that direction then the vector has a positive value (“V”). If there is no current then it has a negative value (“V”). Note that there are many methods for calculating the magnitude of “q” with respect to time, but there is only one method for calculating “V”, i.e., with respect to space.
In the last example, one fixed-size charge was moved from point B to C. The electric field between points A and B was zero. But if Q was moved from point A to C that would create a force on B proportional to the negative of that force. The actual experimental result is not precisely zero, but is extremely small – much smaller than any forces due to any other flow of charge in and out of the circuit. In fact, there are no observable forces in this circumstance (Q = 0), including far more attractive electrical forces, such as those due to ohmic resistance or voltage drop across a resistor.
The electric potential at point A is defined as the work done in moving electric charge from point A to point C, i.e., the measure of the inverse of the charge density between points A and C:
where “q” is the number of coulombs of charge being moved from one place to another.
To obtain an expression that can be used to calculate any quantity with respect to electric potential it is necessary to define a “function” that relates a quantity and its electric potential. For this problem we assume that we know the ratio of Q in relation to C,the distance between points B and C, and that there was no current flowing in direction AB, or normal to it.