**Voltage or Electric Potential Difference**

Before understanding **voltage or potential difference** first we have to understand how a charge particle moves in a uniform static field.

**Voltage Theory**

Let’s assume two parallel plate connect to a battery. The upper plate is connected to positive terminal and the lower plate is connected to negative terminal. So the upper plate is positive charged and lower plate is negative charged. Static electric field is produced between two plates. So the surface charge density of upper plate is σ and surface charge density of lower plate is -σ. The electrical field produced by the only positive plate is the density of surface load divided by twice the space permeability between the plates, i.e.

Like this static electric field generate by negative plate is

So net electric field between two plate is

Lets assume a positive charge particle enters in electric field. If the particle contain q coulomb charge, then electrostatic force applied on particle is

** F**_{e}** = q.E **

Where, E is the vector of the electrical field and constant for a uniform electrical field.

Now acceleration of particles,

Where m is the mass of the particle.

Hence velocity of the particle at any instant is

v_{o} is the initial velocity of particle at entry of uniform electric field

So, Position of particle can be written as

Where p_{o} is the initial position of the particle when enter into a uniform electric field.

The path is function of a parabola. So it can be predicted from function that the motion of charge particle in a uniform electric field is a projectile motion in a parabolic path.

**Electrical Potential Difference and Definition of Voltage**

We can use the electrical field vector to characterize the
space’s static electric field. One can predict the precise features of that
field by observing the motion of loaded particles within an electrical field. If
the field is powerful enough, there will be sharper deflection of a charged
particle in a parabolic path, and if the field is soft, there will be less
deflection. But this is not the practical way to measure an electric field’s
intensity. There is another physical quantity that is much simpler to measure
and also used to characterize an electrical field, and this quantity is known
as the **Electrical Potential Difference.**

The electrical potential V(t) of a position in the electrical field is such that, in order to place a particle of charge q at that position, electrical potential energy is needed, it would be the product of particle q charging and the potential of that position V(t). This is potential U(t) = q. V(t) power.

Volt meter are used to measure the potential difference between two point.

Many have misconcept between Potential and voltage. Many of us believe that the two are the same. But voltage isn’t precisely potential ; it’s measuring the difference between two points in the electrical potential.

**Electrical Potential and Electrical Field Vector**

Both electrical potential and electrical field vector characterize the same thing as electrical field space. They are linked because both the electrical potential and the electrical field vector define an electrical field. DV = – E.ds where the potential distinction between two points separated by the range ds and the vector of the electrical field is E.

**Definition of Potential Difference or Voltage**

In other words, voltage is the distinction between two points in electrical potential energy per unit charge. Voltage is the job to be performed against a static electrical field on a unit charge to move between two points. A voltage that is a measure of the difference in electrical potential is the cause of flowing electrical current in a closed circuit.

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