Formula of Potential Difference Between Two Points

A potential difference is a measure of the electric potential energy per unit charge between two points in an electric field. The electric potential at a point is defined as the work done per unit charge in bringing a test charge from infinity to that point. The electric potential difference between two points is the work done per unit charge in moving a test charge from one point to the other. The formula of potential difference between the two points is:

Work done q = K e Q (1 r1 − 1r2)

Furthermore, the potential difference (voltage) can be calculated by Ohm’s Law with the help of the following equation:

V=I x R

V= Voltage

I= Current

R= Resistance 

What is Electric Potential Energy?

The charges in physics are of two types:

• Positive Charge 

• Negative Charge

Unlike charges always repel, while like charges always attract each other. The force of repulsion or attraction is exerted across an electric field that surrounds the particular charge. Any charge, be it positive or negative, experiences a force of attraction or repulsion that comes in the vicinity of the other charge present.  

Suppose you place a positive charge in an electric field. The electric field center will exert an attractive force on the charge. Moving away from the electric field center involves work to be done, similar to the object lifted against the law of gravity (gravitational force). The forcing away of the charge results in work done, which in turn enhances the electric potential energy of the test charge. 

The work needed to move the charge away depends on the amount of charge. Therefore, electric potential energy experiences an increase as the charge moves away from the electric center of the field.

The energy used in transporting a unit charge from one to the other specific position. In short, every location or point within the electric field possesses a distinct electric potential (function of the distance of the point from the electric field’s charge source)

The Electric Potential Difference Between the Two Points

The electric potential difference between the two points refers to the work done in shifting a charge from one place to another. The potential difference is measured in volts which refer to the shift in the potential energy occurring while transporting one unit charge from one point to another. Volt is equal to one joule per coulomb. 

For example, when the two terminals of a battery having potential differences are used to connect any circuit, the charge from terminal one flows to another until the balance of charge equalises. This process keeps on going until the difference between the two terminals equalises. 

How is the Potential Difference Between Two Points Calculated?

Potential difference between two points is equal to work done / charge.

V=qW

or,  W=V.q 

Ohm’s Law

The potential difference between two points can be calculated using Ohm’s Law.

In electronics, Ohm’s law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. It is named after Georg Simon Ohm, who published his findings in 1827. The law is usually summarised as I = V/R, where I is the current in amps, V is the voltage in volts, and R is the resistance in ohms. This equation forms the basis for many other important electrical equations. 

While calculating the potential difference between two points, the equation can be used as:

V = IR 

Here,

(V) Denotes the potential difference

(I) Denotes the current flowing

(R) Denotes the constant proportionality factor

While calculating the potential difference, Ohm’s Law states that in between the two points of a conductor, the voltage is directly proportional to the current that flows through it until the physical properties remain constant. 

The devices that are used to measure the electric potential difference between the two points are called voltmeters. Voltmeters are the devices used to know the potential difference by measuring the current that flows across the conductors. 

The Difference Between Electric Potential and Potential Difference

Electric potential and potential difference are two important concepts in electricity. Electricity is the result of the flow of electric charges, and these two terms help define some of the key properties of electric charges. Electric potential is a measure of how much work it takes to move a unit of electric charge from one point to another in an electric field. Meanwhile, potential difference is the difference in electric potential between two points. It is this potential difference that allows current to flow through an electrical circuit.

Solved Example:

Question 1 – Calculate the potential difference of a circuit where a current of 30 amperes travels through it. The circuit has a 5 Ohms resistor connected in parallel. Calculate the potential difference of the circuit.

Voltage (V)= (I) Current x Resistance

V= 30 x 5

V= 150

Thus, the potential difference is 150 V

Conclusion

The electric potential difference between two points in an electric field is the work done to move a unit charge from one point to the other. It is a measure of the electric potential energy per unit charge of the system. A positive potential difference means that the charges have more potential energy than a negative potential difference. The electric field is strongest at the points with the greatest potential difference.