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Electric Potential - Definition, Formula, SI Unit

Electrostatic potential refers to the amount of electrical potential energy present at a specific point in space due to the presence of electric charges. It represents how much work would be done to move a unit of positive charge from infinity to that point without causing any acceleration. The unit for electrostatic potential is the volt (V). It’s a fundamental concept in understanding electric fields and plays a crucial role in various electrical applications, from household circuits to complex electronic devices.

In this article, we will learn about electric potential, electric potential energy, and the case of electric potential at a point and much more.

What is Potential?

Potential refers to the amount of “electric push” or “pull” present at a specific location in space. It’s like a measure of how charged particles would feel if they were placed there. Imagine it as a kind of invisible force that tells charged particles how much they want to move or stay put in a given area. So, electric potential helps us understand how charged particles interact with each other and their surroundings in an electric field.

What is Electrostatic Potential?

An electrostatic potential is also known as an electric field potential, an electric potential, or a potential drop.

Electric potential is a measure of the potential energy per unit charge at a specific point in an electric field. It tells us how much work needs to be done to move a positive test charge from infinity to that point. Essentially, it describes the “push” or “pull” a charge would experience at that location. Higher electric potential means more potential energy per charge, while lower electric potential means less. It’s like a landscape where charges naturally move from higher to lower potential, similar to objects rolling downhill due to gravity.

Electrostatic-Potential

Definition of Electric Potential

The amount of work done by a particle or a point charge to move from a reference point (from infinity to distance a) to a specific point without requiring or producing any external or internal acceleration is called an electrostatic potential.

Formula For Electrostatic Potential

The formula for electrostatic potential, often denoted as V, is given by

V = \frac{k \cdot Q}{r} = \frac{1}{4\Pi\varepsilon_0}\frac{Q}{r}

where,

  • V represents the electrostatic potential at a point,
  • k is Coulomb’s constant (a proportionality constant),
  • Q is the magnitude of the point charge creating the electric field, and
  • r is the distance from the point charge to the point of electric po

What is Electric Potential at a Point?

Electric potential at a point is the amount is the work done per unit charge in bringing a positive test charge from infinity to that point in the electric field. Mathematically, electric potential (V) at a point is defined as the ratio of electric potential energy (U) to the charge (q) at that point:

V = U/q

The SI unit of electric potential is the volt (V), which is equivalent to one joule per coulomb (J/C). Electric potential is a scalar quantity, and its sign indicates whether the point is at a higher (positive) or lower (negative) electric potential compared to a reference point.

Potential Due to Point Charge

When you have a point charge, it creates an electric field around it. This electric field has a potential, often called the electrostatic potential, at any point in space around the charge. The formula to calculate this potential due to a point charge (Q) is V = \frac{k \cdot Q}{r} where (V) is the potential, (k) is Coulomb’s constant, (Q) is the magnitude of the point charge, and (r) is the distance from the point charge to the point where you want to find the potential. This formula helps understand how the electric potential changes with distance from the point charge, providing insights into the behavior of electric fields in space.

Electrostatic-potential--due-to-point-charge

Formula for Electric Potential at a Point

The formula for electric potential at a point in an electric field, denoted as V, is:

V = \frac{k \cdot Q}{r}​

Where:

  • V represents the electric potential at the point,
  • k is Coulomb’s constant (a proportionality constant),
  • Q is the magnitude of the point charge creating the electric field, and
  • r is the distance from the point charge to the point where the potential is being measured.

This formula helps determine the electric potential due to a point charge at any location in space, providing a fundamental understanding of electric fields and their effects.

Unit of Electric Potential

The unit of electric potential is the volt (V). It measures the electric potential or voltage difference between two points in an electric field. One volt is defined as the potential difference across a conductor when a current of one ampere dissipates one watt of power.

Volts (v) = Joules (J) / coulomb (C)

Dimension of Electric Potential

The dimension formula of electric potential is ML2T-3A

Factors Influencing Electrostatic Potential

Whether or not a charge is introduced into the electric field does not affect the electric potential. Since the electric potential is a scalar quantity, its only attribute is its magnitude. It is aimless.

Several factors influence electrostatic potential, including:

  • Magnitude of Charge: The electrostatic potential is directly proportional to the magnitude of the charge. Higher charge values result in greater potential.
  • Distance Between Charges: The electrostatic potential decreases as the distance between charges increases. It follows an inverse-square law, meaning that the potential decreases rapidly with increasing distance.
  • Medium: The electrostatic potential can be influenced by the medium between charged objects. Different materials have varying permittivity, affecting how electric fields propagate and interact with charges.
  • Presence of Other Charges: The presence of additional charges in the vicinity can affect the electrostatic potential. Charges can attract or repel each other, altering the overall potential distribution.
  • Geometry of Charge Distribution: The spatial arrangement of charges plays a role in determining the electrostatic potential. The distribution’s symmetry and shape influence the potential’s magnitude and direction.
  • Boundary Conditions: Electrostatic potential can be influenced by boundary conditions, such as conductive surfaces or insulating materials, which can affect charge distribution and field lines.
  • External Fields: External electric or magnetic fields can affect the electrostatic potential in a region by altering the charge distribution or influencing the motion of charges.

What is Electric Potential Energy?

Electric potential energy is the stored energy that results from the position or configuration of charged particles within an electric field. It arises due to the interaction between these charged particles and the electric field in which they are situated. The electric potential energy of a charged particle depends on its position relative to other charged particles and the strength of the electric field.

Electrostatic potential energy formula:

U_E = k \frac{q_1q_2}{r}

where,

  • UE = the electric potential energy
  • q1, q2 = electric charges
  • r = Distance between q1 & q2

Electric Potential and Electric Potential Energy

The electric potential is the electric potential energy per unit charge at a place in space. In other words, electric potential is the total energy a unit test charge would have had at that time; we measure it in volts. However, electric potential energy is provided by a charged particle’s place in an electric field. We measure it in joules.
The relationship between electric potential and electric potential energy is expressed as follows: electric potential energy = charge x electric potential.

Basis of difference

Electric Potential

Electric Potential Energy

Dependence on Charge

It depends only on the source charge(s) creating the electric field and the distance from the point of interest.

It depends not only on the charges creating the electric field but also on the test charge or system of charges experiencing the field.

Nature

It is a scalar quantity, representing the intensity of the electric field at a given point.

It is a scalar quantity, representing the stored energy in a system of charges due to their configuration in an electric field.

Representation

It represents the electric field intensity at a particular point.

It represents the stored energy in a system of charges.

Relation

It is related to electric potential energy per unit charge, as V = U/q, where V is electric potential, U is electric potential energy, and q is charge.

It contributes to the electric potential, as the electric potential at a point is directly related to the electric potential energy per unit charge at that point.

Calculation

It’s calculated by dividing the electric potential energy by the amount of charge present.

It’s calculated by summing up the work done in bringing individual charges together from infinity to their respective positions.

Conclusion

Electric potential is one of the crucial concepts occupying the sphere of electromagnetism, providing access to the interactions of charged particles within electric fields. Discovered by the measurement of the influence of “pushing” or “pulling” charges experienced at different places in space, the electric potential uncovers the nature of electric interaction and makes some of the physical matters less complicated. By exploring the electric potential’s essence and its integral part—electric potential energy—we have opened a path to understanding some of the fundamental forces regulating the course of existence on Earth and seeding inspiration for new technological solutions.

Also, Check

Solved Examples on Electrostatic Potential

Example 1: Calculate the electric potential at a point located 4m away from a point charge of 5— μC.

Solution:

Given:

Point charge = 5μC = 5 × 10 -6 C
Distance from the point charge to the point where the potential is to be calculator: r= 4m
Vacuum permittivity ε0 = 8.854×10 −12 C2 /N⋅m2
Electric potential formula: V = KQ/r

1. Convert the charge to coulombs if necessary: Q = 5 × 10 -6 C

2. Use the formula for electric potential: V = K.q/r

3. Substitute the given values: V = (8.99 × 10 9) × (5 × 10 -6)/4m

4. Calculate the result: V = (8.99 × 10 9) × (5 × 10 -6)/4

⇒ V = 11.2375 × 10 3 V

5. Convert the result to kilovolts (kV): V = 11.2375 kV

The electric potential at a point located 4m away from a point charge of 5μC is 11.2375kV

Example 2: Determine the electric potential at 0.001 m from a charge of 2pC.

Solution:

By the formula,

V = kq/r

we can conclude that, by :

K= 9 × 10 9

1p = 1 × 10 -12 (picometre)

hence,

V = 9 × 109(2 × 10 -12)/(0.001) = 18 volts

Example 3: If a second charge (-2pC) was the same distance from the point of interest as the first charge, find the total electric potential at that point.

Solution:

The total potential is the algebraic sum of the potential caused by each charge:

V = Σkq/r

Since the distances are the same for each charge, but the sign is opposite, the total potential is zero in this case.

Example 4: Two charges are located on the corners of a rectangle with a height of 0.05 m and a width of 0.15 m. The first charge (q1= -5×10-6 C) is located at the upper left-5-hand corner, while the second charge (q2 = +2.0 × 10-6 C) is at the lower right-hand corner. Determine the electric potential at the upper right-hand–hand corner of the rectangle.

Solution:

To calculate the electric potential, we will sum up the electric charges present in the right-hand corner of the rectangle:

Given :
K = 9 × 10 9 N.m2/c2
q1 = -5 × 10 -6 C
q2 = +2.0 × 10 -6 C
r1 = 0.05m, r2 = 0.15m

V = Σ(kq/r)

V = k[(-5×10-6/0.15) + (2×10-6/0.05)]

V = 60000 volts

Example 5. What is the potential difference for a point at the right-hand corner (call it point A) of the rectangle in question #4 relative to the lower left-hand corner (call it point B)?

Solution:

VA = 60000 volts

as the value of the electric potential at the lower left corner is asked
hence here,
r1 = 0.15m, and r2 = 0.05m

VB = k[(-5×10-6/0.05) + (2×10-6/0.15)] = -780000 volts

ΔV = VA – VB = 60000 – (-780000) = 840000 volts

Therefore, the Potential difference between points A & B is 840000 V.

Practice Problems on Electrostatic Potential

Q1. A point charge of +3μC is located at the origin. Calculate the electric potential at a point 5 meters away from the charge.

Q2. Two point charges, +6 °C and −4 °C, are placed 2 meters apart in air. Determine the electric potential at a point midway between the charges.

Q3. A uniform electric field of magnitude 200N/C exists in the positive x-direction. Calculate the electric potential difference between two points A and B that are 3m apart along the x-axis.

Q4. A charge distribution creates an electric potential of 50 volts at a distance of 4m from the center of the distribution. Determine the total charge of the distribution if it is spherically symmetric.

Q5. A capacitor has a capacitance of 20μF and is connected to a 100V battery. Calculate the electric potential difference across the plates of the capacitor.

Frequently Asked Questions on Electrostatic Potential

Is the electric potential dependent on the charge (positive or negative)?

Yes, the potential depicts the +\- signs upon the charge of the Q given.

Is the potential zero when the electric field is zero?

No, the potential is not dependent upon the electric field.

With the use of electric potential, can many charges be taken at the same time from infinity?

No, only one charge can be taken from infinity in a specific space and time.

Is there electric potential energy for assembling the unit and charging it around it without using external force?

Yes, the energy needed for the work done to assemble the charges is called self-energy.

What is meant by electrostatic potential?

Electrostatic potential represents the work done in bringing a unit positive charge from infinity to that point in the field without acceleration. It indicates the electrical potential difference between different points in space due to the presence of electric charges.

Why potential at infinity is zero?

The potential at infinity is considered zero because it serves as a reference point or baseline for measuring electric potential in a system. At infinity, the influence of any electric charge becomes negligible, and the electric potential due to all charges effectively diminishes to zero.

What is the SI unit of electric potential?

The SI unit of electric potential is the volt (V). It is defined as one joule per coulomb (1 J/C), representing the amount of electric potential energy per unit charge. The volt is the standard unit used to measure electric potential difference or voltage in electrical systems and circuits.


 


Reffered: https://www.geeksforgeeks.org

Class 12

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