 # Electric Potential - Point Charge  View Notes

What is Electric Potential and How it Works?

The electric potential, or voltage, is the distinction in potential energy per unit charge between two areas in an electric field. At the point when we discussed the electric field, we selected a location and afterward asked what the electric power/force would do to an imaginary positively charged particle if we placed one there.

To measure the electrical potential at a selected spot, we ask how much the electrical possible energy of an imaginary positively charged particle would change if we moved it there. Much the same as when we discussed the electric field, we don't really need to put a positively charged particle at our selected spot to know how much electrical potential energy it would have.

Reason for Change

We realize that the measure of charge we are pushing or pulling (and whether it is positive or negative) has any kind of effect on the electrical potential energy if we move the molecule to a selected spot. That is the reason physicists utilize a single positive charge as our imaginary charge to try out the electrical potential at some random point. That way we just need to stress over the measure of charge on the plate, or whatever charged item we're considering.

Impact on Electric Potential

Suppose we have a negatively charged plate. We realize that a positively charged molecule will be pulled towards it. That implies we realize that if we select a spot close to the plate to put our imaginary positively charged particle, it would have a smidgen of electrical potential energy, and if we select a spot further away, our imaginary positively charged molecule would have increasingly more electrical energy. So we can say that close to the negative plate the electrical potential is low, and further from the negative plate, the electrical potential is high.

Electric potential is, for the most part, a trait of the electric field. It is free of the reality whether a charge ought to be set in the electric field or not. Electric potential is a scalar quantity. At point charge +q there is consistently a similar potential at all points with a distance r.

Electric Potential Due to Point Charge

The electric potential at a point in an electric field is characterized as the measure of work done in moving a unit positive charge from infinity to that point along any path when the electrostatic powers/forces are applied. Assume that a positive charge is set at a point. The charge set by then will apply a power/force because of the presence of an electric field. The electric potential anytime at a distance r from the positive charge +q is appeared as:

It is given by the formula as stated,

V=1*q/4πϵ0*r

Where,

The position vector of the positive charge = r

The source charge = q

As the unit of electric potential is volt,

1 Volt (V) = 1 joule coulomb-1(JC-1)

At the point when work is done in moving a charge of 1 coulomb from infinity to a specific point because of an electric field against the electrostatic power/force, at that point it is supposed to be 1 volt of the electrostatic potential at a point.

Electric Potential Because of Multiple Charges

When there is a

q1, q2, q3,… .qn as a group of point charges

And is kept at

Distance r1, r2, r3,… … rn,

We can get the electrostatic potential at a specific point. We can locate the electrostatic potential at any point because of every individual charge by considering different other charges as absent. We at that point include all the charges mathematically.

Henceforth, the electric potential at a point because of a group of point charges is the mathematical total of all the potentials because of individual charges.

It is stated as,

V = $\frac{1}{4π∊₀}$ $\sum_{i=1}^{n}$ $\frac{q_{i}}{r_{i}}$

1. Explain the Electric Potential Derivation?

Let us consider q1 as a charge. Take the assumption that they are placed at a distance 'r' from one another. The absolute electric potential of the charge is characterized as the total work done by an external power in carrying the charge from infinity to the given point.

We can compose it as, - ∫ (ra→rb) F.dr = – (Ua – Ub)

Here, we see that the point rb is available at infinity and the point ra is r.

By substituting the values, we will get, - ∫ (r →∞) F.dr = – (Ur – U∞)

As we realize that Uinfity is equivalent to zero.

So, - ∫ (r →∞) F.dr = - UR

Utilizing Coulomb's law, between the two charges we can compose:

⇒ - ∫ (r →∞) [-kqqo]/r2 dr = - UR

Or then again, - k × qqo × [1/r] = UR

That means, UR = - kqqo/r

2. What are the Two Methods of Electric Potential Formula?

A charge put in an electric field has potential energy and is estimated by the work done in moving the charge from infinity to that point against the electric field. In the event that two charges q1 and q2 are isolated by a distance d, the electric potential energy of the framework are;

U = 1/(4πεo) × [q1q2/d]

The two methods for the electric potential formula are as follows:

Method 1:

At any point around q as a point charge, the electric potential is given as:

V = k x [q/r]

Where,

V indicates electric potential energy

k indicates Coulomb constant which values at 9.0 x 109 N

q indicates point charge

r indicates distance

Method 2:

As per Coulomb’s Law

The electrostatic potential between any two discretionary charges q1, q2 isolated by distance r is given by Coulomb's law and scientifically composed as:

U = k × [q1q2/r2]

Where,

The electrostatic potential energy is indicated by the U,

The two charges are q1 and q2

Note: At infinity, the electric potential is zero (as r = ∞ in the above equation).

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