Electric Potential Due to Multiple Charges

In this article, we will learn about the object’s electric potential, the factors that affect an object’s electric potential, electric potential due to a point charge, and electric potential due to multiple charges.

The electric potential refers to the quantity of work required to shift a charge to a certain specific point from a reference point against the electric field. Majorly, the electric potential of an object depends on these factors:

● The electric charge is carried by the object.

●The relative position of an object with other objects charged electrically.

What is Electric Potential Energy?

Electric Potential Energy refers to the amount of energy gained by an object when moved against an electric field. When an object is shifted from one point to another across the electric field, it acquires some energy known as the energy potential of an object. As mentioned above, the electric potential of an object depends on these factors – the electric charge an object is carrying and the relative position with other charged objects. The object’s electric potential defines the power of the electric field, which is independent of the placement of charge within the electric field. In simple terms, the presence or absence of the charge in the electric field does not affect the power of the electric field. 

How Do We Obtain Electric Potential of the Charge?

To obtain a charge’s electric potential: 

Divide the Potential Energy by the quantity of charge. 

At +q (point charge), the electric potential remains the same at every point with r (distance)

Electric Potential Due to a Point Charge

Let’s take a case where a positive charge is placed at a particular point. Due to the presence of the electric field, the charge will exert a force at that point. Therefore, when a charge, i.e., positive, is transported to a certain point in the electric field from infinity by applying electrostatic forces, it is called electric potential. The electric potential, r from +q at any individual point, can be shown as:

V= (1/4π∈0) q/r

r= the distance

q= source charge

As volt is the unit of electrical potential, 

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

When a charge of 1 coulomb is moved from infinity to a particular point against the electrostatic force, it is referred to as 1 volt of the electric potential at a point. 

Electric Potential Due to Multiple Charges

The electric potential at any given point can be obtained when a system of the point charges. For example, a group – Q1, Q2, Q3…..Qn, is placed at a distance, say, r1, r2, r3,…..rn.

Now, when due to each individual charge, the electrostatic potential can be found at any point by considering the other charges are not present, each charge shall be added algebraically. 

It is given as:

Therefore, the electric potential due to multiple charges can be explained as the sum derived from adding the potentials due to individual charges.  

Important Points to be Noted in Terms of Electric Potential 

– At the location halfway in the middle of two opposite and equal charges, the electric potential is zero but the electric field is not.

– If in pushing one coulomb of the charge against the electric field, one joule of work is done, the electric potential, in this case, will be one volt.

– When a negative charge is moved from one point, say A to another charge, say B, the electric potential increases.

– To determine the electric potential at a place, infinity is the reference level used. The force on a test charge is zero at the reference level.

– Earth is so enormously massive that subtracting or adding a charge to it does not affect its electrical state.

– The work done while a unit’s positive charge is transported from point A to B is said to be “work done”. If the effort is ‘W’ and the unit charge is ‘Q’, then the potential difference between two different points is V=W/Q

Conclusion

The real-life systems barely use single charges. Almost every arrangement or electrical world uses multiple charges. Therefore, the algebraic sum of the potential of individual charges at a point gives the total potential of the point charges at a point in a system. In other words, electric potential due to multiple charges is more in use as compared to electric potential due to a point charge. Summing up, the electric potential of a charge or system of charges is the total work done when a charge or multiple charges are transported from infinity to the current configuration. Electric potential, just like some other concepts of physics, varies with distance. In simple terms, electric potential rises with the decrease in distance and decreases with the increase in distance. Hence, following the formula, electric potential varies inversely with distance.