Electric Potential

Electric Potential

Edited By Vishal kumar | Updated on Jul 02, 2025 05:34 PM IST

Electric potential is like the driving force behind electricity. It determines how electric charges behave and move through wires and circuits. Think of it as the push or energy that enables electricity to flow from one point to another. This push, measured in joules per coulomb, explains why batteries can power devices, lights turn on when you flip a switch, and appliances work when plugged in. Understanding electric potential helps us comprehend how electricity operates in our everyday lives, influencing everything from powering gadgets to lighting up our homes.

This Story also Contains
  1. Electric Potential
  2. Solved Example Based On Electric Potential
  3. Summary
Electric Potential
Electric Potential

In this article, we will cover the concept of Electric Potential. This concept is in the class 12th electrostatic chapter. It is not only essential for board exams but also for competitive exams like the JEE Main, NEET, and other entrance exams such as SRMJEE, BITSAT, WBJEE, BCECE and more. Over the last ten years of the JEE Main exam (from 2013 to 2023), a total of six questions have been asked on this concept. And for NEET two questions were asked from this concept. It is a very important topic for understanding the electrostatic chapter and many questions are asked about this concept.

Electric Potential

In an Electric field Electric potential V at a point, P is defined as work done per unit charge in changing the position of test charge from some reference point to the given point.

Note-usually reference point is taken as infinity and potential at infinity is taken as Zero.

We know that
Wext=Fextdr

Since
Wext =ΔU and ΔKE=0Fer all time Fnet =0Fext +Fsystem =0 i.e Fext =Fsystem V=Wext q0=Fext drq0=Fsystem drq0

where

V Electric potential
- It is a scalar quantity.
SI Unit JC= volt while the CGS unit is stat volt
1 volt =1300 stat volt.
- Dimension -
[V]=[Wq0]=[ML2T2AT]=[ML2T3A1]

Electric Potential at a Distance 'r'

If the Electric field is produced by a point charge q then

F=Kqq0r2

Using
V=Wext q0=Fext drq0=Fsystem drq0V=Kqr at r=V=0=Vmax

Electric Potential difference

In the Electric field, the work done to move a unit charge from one position to the other is known as the Electric Potential difference.

If the point charge Q is producing the field

Points A and B are shown in the figure.

VA= Electric potential at point A
VB= Electric potential at point B


rB the distance of charge at B
rA distance of charge at A
ΔV= The Electric potential difference in bringing charge q from point A to point B in the Electric field produced by Q.
ΔV=VBVA=WABqΔV=KQ[1rB1rA]

Superposition of Electric potential

Statement- Total electric potential at a given point in space due to all the charges placed around it is the scalar or algebraic addition of electric potential due to individual charges at that point.

i.e

The net Electric potential at a given point due to different point masses (Q1,Q2,Q3…) can be calculated by doing a scalar sum of their individual Electric potential.

V=V1+V2+V3+=kQ1r1+kQ2r2+k(Q3)r3+=14πε0Qiri


  • Electric Potential due to Continuous charge distribution

V=dV=dq4πε0r

  • Graphical representation
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As we move on the line joining two charges then the variation of Potential with distance is given below.

Zero Potential Due to a System of a Two-Point Charge

1. For internal point

(It is assumed that |Q1|<|Q2| )

Let at P,V is zero
VP=0Q1x1=Q2(xx1)x1=x(Q2/Q1+1)

If both charges are like then the resultant potential is not zero at any finite point.

2. For external point

Let P, V be zero

VPQ1x1=Q2(x+x1)x1=x(Q2/Q11)

For More Information On Electric Potential, Watch The Below Video:

Solved Example Based On Electric Potential

Example 1: Two thin wire rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are +Q and -Q The potential difference between the centers of the two rings is

1) zero
2) Q4πε0[1R1R2+d2]
3) QR4πε0d2
4) Q2πε0[1R1R2+d2]

Solution:

As we learnt in

Electric Potential -

V=wq0

- wherein

w - work done

q0 - unit charge.

VA=14πε0QR14πε0QR2+d2VB=14πε0(Q)R+14πε0QR2+d2

VAVB=1×Q4πε0[2R2R2+d2]=Q2πε0[1R1R2+d2]

Hence, the answer is option (4).

Example 2: The figure shows three points A,B and C in a region of the uniform electric field E. The line AB is perpendicular and BC is parallel to the field lines. Then which of the following holds good? Where VA,VB and VC represent the electric potential at points A,B and C respectively.

1) VA=VB=VC
2) VA=VB>VC
3) VA=VB<VC
4) VA>VB=VC

Solution:

As we have learned,

Equipotential Surface -

All Points have the same Potential.

Electric lines of force flow from higher potential to lower potential so,

VA=VB>VC

Hence, the answer is option (2).

Example 3: Four charges +Q,Q,+Q,Q are placed at the corners of a square taken in order. At the centre of the square.

1) E=0,V=0
2) E=0,V0
3) E0,V=0
4) none of these

Solution:

As we learned

Potential of a System of Charge -

V=i=1i=nkQiri

At centre

E=0

and V = 0 due to symmetry structure.

Example 4: A charge Q is uniformly distributed over a long rod AB of length L, as shown in the figure. The electric potential at the point O lying at a distance L from the end A is :

1) QIn24πϵ0L
2) Q8πϵ0L
3) 3Q4πϵ0L
4) Q4πϵ0LIn2

Solution:

As we discussed in

Potential Difference -

VBVA=wq

Charge on the element
dQ=QLdx

Potential at 0
dV=14πϵodQx=14πϵoQLxdxdV=L2L14πϵoQLxdx=14πϵoQL[lnx]L2LV=Qln24πϵoL

Hence, the answer is option (1).

Example 5: Two points P and Q are maintained at the potentials of 10 V and 4 V respectively. The work done in moving 100 electrons from P to Q is:

1) -9.60 x 10-17 J

2) 9.60 x 10-17 J

3) -2.24 x 10-16 J

4) 2.24 x 10-16 J

Solution:

As we learnt in

Potential Difference -

VBVA=WqW=(100e)(VQVP)=(100×1.6×1019)(14V)=2.24×1016 J

Hence, the answer is option (4).

Summary

Electric potential, otherwise known to most as voltage, is the potential energy available at a particular point of an electric field per unit of charge. It is measured in volts, thereby showing the work per unit charge that is required to move a charge between two points. High electric potential simply means that there is more potential energy 'available' to move charges—it is referred to as the electromotive force, able to drive current through a circuit. Knowledge of electric potential is very important in the design of electrical systems, ranging from simple circuits to large-scale power grids, and also for the safe and efficient use of electrical devices.

Frequently Asked Questions (FAQs)

1. What is electric potential?
Electric potential is the amount of electric potential energy per unit charge at a point in an electric field. It represents the work done to move a unit positive charge from infinity to that point, measured in volts (V).
2. How is electric potential different from electric potential energy?
Electric potential is a property of a point in space and is measured in volts (V), while electric potential energy is the energy possessed by a charge at that point and is measured in joules (J). Potential energy depends on both the charge and the potential.
3. Why doesn't electric potential depend on the test charge?
Electric potential is defined as the potential energy per unit charge, so it's independent of the test charge. It only depends on the configuration of the source charges creating the electric field.
4. Can electric potential be negative?
Yes, electric potential can be negative. It depends on the choice of reference point (usually infinity) and the nature of the source charges. Negative potential means work is done by the field to bring a positive test charge from infinity to that point.
5. What's the relationship between electric field and electric potential?
Electric field is the negative gradient of electric potential. In other words, the electric field points in the direction of decreasing potential, and its magnitude is the rate of change of potential with distance.
6. Why do we use the concept of electric potential?
Electric potential is useful because it's a scalar quantity, making calculations simpler than working with vector fields. It also allows us to analyze energy changes in electric systems without considering the specific path taken by charges.
7. How does electric potential vary with distance from a point charge?
For a point charge, electric potential varies inversely with distance. It follows the equation V = kQ/r, where k is Coulomb's constant, Q is the charge, and r is the distance from the charge.
8. What happens to electric potential inside a conductor?
Inside a conductor in electrostatic equilibrium, the electric potential is constant. This is because any potential difference would create an electric field, which would move charges until equilibrium is restored.
9. How do you calculate the work done in moving a charge between two points?
The work done is equal to the charge multiplied by the potential difference between the two points: W = q(V₂ - V₁), where q is the charge, and V₂ and V₁ are the potentials at the final and initial points, respectively.
10. What's an equipotential surface?
An equipotential surface is a surface where all points have the same electric potential. No work is done in moving a charge along an equipotential surface. These surfaces are always perpendicular to electric field lines.
11. Why are equipotential surfaces important?
Equipotential surfaces help visualize the electric potential in space. They're useful for understanding field geometry and for simplifying calculations, as movement along these surfaces requires no work.
12. How does the shape of equipotential surfaces relate to the strength of the electric field?
The spacing between equipotential surfaces indicates the strength of the electric field. Closely spaced equipotential surfaces represent a strong electric field, while widely spaced surfaces indicate a weak field.
13. What's the electric potential due to a dipole?
The electric potential due to a dipole varies as 1/r² at large distances, where r is the distance from the dipole. It depends on the dipole moment and the angle relative to the dipole axis.
14. How does superposition apply to electric potential?
The principle of superposition applies to electric potential: the total potential at a point due to multiple charges is the algebraic sum of the potentials due to individual charges.
15. What's the significance of zero potential?
Zero potential is a reference point, often chosen to be at infinity or at the Earth's surface. It's arbitrary but necessary for defining potential differences, which are what matter in calculations.
16. How does electric potential relate to voltage?
Voltage is the difference in electric potential between two points. When we talk about the "voltage" of a battery, we're referring to the potential difference between its terminals.
17. Why doesn't a moving charge in a uniform electric field have constant potential energy?
A moving charge in a uniform electric field experiences a change in potential energy because it moves to points of different potential. Its kinetic energy changes as potential energy changes, maintaining constant total energy.
18. How do you find the direction of electric field from equipotential surfaces?
The electric field is perpendicular to equipotential surfaces and points in the direction of decreasing potential. The field direction is from higher potential to lower potential.
19. What's the relationship between work and potential in conservative fields?
In a conservative field like the electrostatic field, the work done in moving a charge between two points is independent of the path taken and depends only on the potential difference between those points.
20. How does the concept of electric potential apply to lightning?
Lightning occurs when there's a large potential difference between clouds or between clouds and the ground. The discharge equalizes this potential difference, releasing energy in the form of light, heat, and sound.
21. Why is the electric field zero inside a conductor but the potential isn't necessarily zero?
Inside a conductor in electrostatic equilibrium, charges redistribute to cancel out any internal field. However, the potential can be non-zero and constant throughout the conductor, depending on its overall charge and surroundings.
22. How does electric potential energy relate to stability in atomic systems?
In atomic systems, stability is associated with minimum potential energy configurations. Electrons in atoms tend to occupy states of lower potential energy, which contributes to the stability of atomic structures.
23. What's the significance of the electron volt (eV) in discussing electric potential?
An electron volt is the energy gained by an electron moving through a potential difference of 1 volt. It's a convenient unit in atomic and particle physics, where energies are often small compared to everyday scales.
24. How does the concept of electric potential apply to capacitors?
In a capacitor, electric potential difference between the plates creates an electric field. The energy stored in a capacitor is related to this potential difference and the capacitor's capacitance.
25. Why doesn't the electric potential inside a hollow conductor depend on the shape of the conductor?
The electric potential inside a hollow conductor is constant and equal to the potential at the surface, regardless of the conductor's shape. This is because the electric field inside is zero, so there's no potential gradient.
26. How does grounding affect electric potential?
Grounding connects an object to the Earth, which is conventionally assigned a potential of zero. This equalizes the potential of the object with the Earth, effectively "zeroing" its potential relative to the ground.
27. What's the relationship between electric potential and electrical safety?
Electrical safety often involves managing potential differences. Large potential differences can cause harmful current flow through the body. Safety measures like insulation and grounding help prevent exposure to dangerous potential differences.
28. How does the concept of electric potential apply to batteries?
A battery maintains a potential difference between its terminals through chemical reactions. This potential difference, or voltage, drives current in circuits connected to the battery.
29. Why isn't it possible to define an absolute electric potential for a single point charge?
Electric potential is always defined relative to a reference point (usually infinity). For a single point charge, we can calculate potential differences, but an absolute potential value doesn't have physical meaning without a reference.
30. How does the principle of electric potential apply in electrochemistry?
In electrochemistry, differences in electric potential drive electron transfer reactions. The potential difference between electrodes in an electrochemical cell determines the direction and extent of chemical reactions.
31. What's the significance of the electric potential at infinity?
The electric potential at infinity is often chosen as the reference zero point. This choice simplifies calculations and allows for consistent comparison of potentials in different systems.
32. How does electric potential relate to energy conservation in electrostatic systems?
The concept of electric potential ensures energy conservation in electrostatic systems. The total energy (kinetic plus potential) of a charge moving in an electrostatic field remains constant, with changes in potential energy balanced by changes in kinetic energy.
33. Why do birds sitting on high-voltage power lines not get electrocuted?
Birds on power lines don't get electrocuted because they're at a single electric potential. Electrocution requires a potential difference, which would occur if the bird touched the ground or another wire at a different potential simultaneously.
34. How does the concept of electric potential apply to Van de Graaff generators?
Van de Graaff generators create high electric potentials by accumulating charge on a metal sphere. The potential of the sphere increases as more charge is added, leading to dramatic effects like hair standing on end when someone touches the sphere.
35. What's the relationship between electric potential and electrical pressure in circuits?
Electric potential difference in circuits is often described as "electrical pressure." Just as water pressure drives water flow, potential difference (voltage) drives current flow in electrical circuits.
36. How does the concept of electric potential apply to solar cells?
Solar cells generate a potential difference when exposed to light. This potential difference, created by the photovoltaic effect, can drive current in an external circuit, converting light energy to electrical energy.
37. Why is the electric potential constant along a wire in a circuit, even though current is flowing?
In an ideal wire with no resistance, the electric potential is constant along its length because there's no energy loss. In real wires, there's a small potential gradient due to resistance, but it's often negligible for good conductors.
38. How does electric potential relate to the concept of voltage drop in circuits?
Voltage drop refers to the decrease in electric potential across a component in a circuit. It represents the electrical energy converted to other forms (like heat or light) as current flows through the component.
39. What's the significance of the electric potential difference in nerve cell signaling?
In nerve cells, the potential difference across the cell membrane (membrane potential) is crucial for signal transmission. Changes in this potential, called action potentials, allow information to propagate along neurons.
40. How does the concept of electric potential apply to electrostatic precipitators?
Electrostatic precipitators use high voltage (high electric potential) to create strong electric fields. These fields charge and attract particles from gases, cleaning industrial emissions by exploiting principles of electric potential and force.
41. Why doesn't the electric potential inside a Faraday cage depend on external electric fields?
A Faraday cage shields its interior from external electric fields. Charges on the cage's surface redistribute to cancel the external field, resulting in zero field and constant potential inside, regardless of external potentials.
42. How does electric potential relate to the breakdown voltage of insulators?
The breakdown voltage is the minimum voltage (potential difference) that causes an insulator to become conductive. It represents the point where the electric field becomes strong enough to ionize atoms in the insulator, creating a conductive path.
43. What's the relationship between electric potential and the work function in photoelectric effect?
The work function, the minimum energy needed to eject an electron from a material's surface, is related to the material's electric potential. Overcoming this potential barrier requires photons with energy greater than the work function.
44. How does the concept of electric potential apply to particle accelerators?
Particle accelerators use large electric potential differences to accelerate charged particles. The potential difference determines the kinetic energy gained by the particles, allowing control over their speed and energy for experiments.
45. Why is the electric potential inside a thundercloud not uniform?
The electric potential inside a thundercloud varies due to charge separation processes. Updrafts separate charges, creating regions of different potential that can lead to lightning discharges when the potential difference becomes large enough.
46. How does electric potential relate to the concept of electrical ground in circuit design?
In circuit design, electrical ground serves as a reference point for measuring potentials. It's typically assigned a potential of zero, allowing other potentials in the circuit to be measured relative to this common reference.
47. What's the significance of the electric potential difference in electroplating processes?
In electroplating, the electric potential difference between electrodes drives the movement of metal ions. The magnitude of this potential difference affects the rate and quality of the plating process.
48. How does the concept of electric potential apply to the design of surge protectors?
Surge protectors are designed to limit the electric potential (voltage) applied to sensitive electronics. They redirect excess potential to ground when the voltage exceeds a safe threshold, protecting devices from damage.
49. Why doesn't the electric potential of Earth change significantly despite constant lightning strikes?
The Earth's enormous size and conductivity allow it to quickly distribute and neutralize charges from lightning strikes. This large capacitance means that even numerous strikes cause only negligible changes to the Earth's overall electric potential.
50. How does the concept of electric potential apply to the function of capacitive touch screens?
Capacitive touch screens detect changes in electric potential caused by a finger's touch. The screen's surface acts as one plate of a capacitor, and the finger as another. The touch alters the local electric potential, which is detected and interpreted as input.

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