Electric Field

Electric Field

Edited By Vishal kumar | Updated on Jul 02, 2025 05:51 PM IST

When we circle around a charged particle or object charged particles are forced. It is like an invisible force field that can make other charges. The formation or end of such a field’s force lines represents its power and orientation respectively; they also indicate the path along which there would be motion if there were a positive test charge within the given field. The understanding of electric forces operating by the use of electric field lines is a major aspect of physics.

This Story also Contains
  1. Electric field and electric lines of force:
  2. Electric Field Intensity:
  3. Electric field due to a point charge:
  4. Solved Examples Based on Electric Field
  5. Summary
Electric Field
Electric Field

In this article, we will discuss the electric field. An electric field is considered one of the main ideas that is very necessary to understand different things that happen around us both in the past and the present day. This is the area which surrounds a charged particle and through which other charges feel the force. In order to pass NEET or JEE Main exams, it is necessary to study what the electric field means since it is needed when studying other topics such as electrostatics and electromagnetism. Over the last ten years of the JEE Main exam (from 2013 to 2023), a total of seventeen questions have been asked on this concept. And for NEET three questions were asked from this concept.

Electric field and electric lines of force:

The space around a charge in which another charged particle experiences a force is said to have an electric field in it.

Electric Field Intensity:

The electric field intensity at any point is defined as the force experienced by a unit of positive charge placed at that point.

$
E=\frac{F}{q_0}
$

where F is the force experienced by q 0 . The SI unit

$
\frac{\text { Newton }}{\text { Columb }}=\frac{\text { Volt }}{\text { meter }}=\frac{\text { Joule }}{\text { Coulomb } \times \text { Meter }}
$


The dimensional formula is $\left[M L T^{-3} A^{-1}\right]$

The electric field is a vector quantity and the positive charge is away from the charge and for the negative charge, it is towards the charge.

Electric field due to a point charge:

Consider a point charge placed at the origin O. Let a test charge q0 is placed at P which is at a distance r from O. Force F on test charge q0 is


$
F=\frac{1}{4 \pi \epsilon_0} \frac{q q_0}{r^2} \hat{r}
$


The electric field at point $P$ due to $q$ is

$
E=\lim _{q_0 \rightarrow 0} \frac{F}{q_0}=\lim _{q_0 \rightarrow 0} \frac{1}{q_0} \frac{1}{4 \pi \epsilon_0} \frac{q q_0}{r^2} \hat{r}=\frac{1}{4 \pi \epsilon_0} \frac{q}{r^2} \hat{r}
$

(As $\mathrm{q}_0$ tends to zero the electric field produced by q is not affected by $\mathrm{q}_0$.)
The magnitude of the electric field

$
E=\frac{1}{4 \pi \epsilon_0} \frac{q}{r^2}
$

Electric field due to a system of charge

The electric field obeys the superposition principle. That is the electric field due to a system of charge at a point is equal to the vector sum of all the electric fields.

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Solved Examples Based on Electric Field

Example 1: The electric field inside a spherical shell of uniform surface charge density is

1) Zero

2) Constant, less than zero

3) Directly proportional to the distance from the centre

4) None of the above

Solution:

Electric Field

The space around a charge in which another charged particle experiences a force is said to have an electric field in it.

wherein

All charge resides on the outer surface so that according to Gauss's law, the electric field inside a shell is zero.

Example 2: If $E$ is the electric field intensity of an electrostatic field, then the electrostatic energy density is proportional to
1) $E$
2) $E^2$
3) $\frac{1}{E^2}$
4) $E^3$

Solution:

Electric Field

The space around a charge in which another charged particle experiences a force is said to have an electric field in it.

wherein


Electrostatic energy density $\frac{d U}{d V}=\frac{1}{2} K \varepsilon_0 E^2$

Hence, electrostatic energy density is proportional to $E^2$.

The correct option is (2).

Example 3: A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge Q (having a charge equal to the sum of the charges on the 4 µF and 9 µF capacitors), at a point distant 30 m from it, would equal :

1) 240 N/C

2) 360 N/C

3) 420 N/C

4) 480 N/C

Solution:

Series Grouping

$\frac{1}{C_{\mathrm{eq}}}=\frac{1}{C_1}+\frac{1}{C_2}+\cdots$

wherein

Parallel Grouping

$C_{\mathrm{eq}}=C_1+C_2+\cdots$

wherein

Electric Field Intensity

$\vec{E}=\frac{\vec{F}}{q_0}=\frac{k Q}{r^2}$

wherein

$3 \mu F$ and $9 \mu F$ are in parallel combinations so their equivalent capacitance is

$
=3+9=12 \mu f
$


Now $4 \mu F$ and $12 \mu F$ are in series so their equivalent capacitance

$
=\frac{4 \times 12}{16}=3 \mu F
$

Charge on $3 \mu F=(3 \mu f) \times(8 V)=24 \mu C$
$\therefore$ Charge on $4 \mu F$ and $12 \mu F$ are same and it is $(24 \mu C)$ as they are in series

Charge on $9 \mu F=\frac{9}{9+3} \times 24 \mu F=18 \mu C$
Now required charge on $\mathrm{Q}=$ charge on $4 \mu F+$ charge on $9 \mu F$

$
\begin{gathered}
\therefore Q=[24+18] \mu C=42 \mu C \\
\therefore E=\frac{1}{4 \pi \epsilon_o} \frac{Q}{r^2} \Longrightarrow E=9 \times 10^9 \times \frac{42 \times 10^{-6}}{(30)^2}=420 N C^{-1}
\end{gathered}
$

Example 4: A thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net field $\vec{E}$ at the centre $O$ is:

1) $\frac{q}{2 \pi^2 \varepsilon_0 r^2} \hat{j}$
2) $\frac{q}{4 \pi^2 \varepsilon_0 r^2} \hat{j}$
3) $-\frac{q}{4 \pi^2 \varepsilon_0 r^2} \hat{j}$
4) $-\frac{q}{2 \pi^2 \varepsilon_0 r^2} \hat{j}$

Solution:

Electric Field Intensity

$\vec{E}=\frac{\vec{F}}{q_0}=\frac{k Q}{r^2}$

wherein


$
\begin{aligned}
& \lambda=\frac{d q}{d l} \\
& d q=\lambda \cdot d l[d l=r d \theta] \\
& d E=\frac{1}{4 \pi r \varepsilon_0} \frac{d q}{r^2} \\
& =\frac{\lambda r d \theta}{4 \pi \varepsilon_o r^2}
\end{aligned}
$

The net electric field at $O$ is

$
\begin{aligned}
& E=\int_o^\pi d E \sin \theta(-\hat{j})=\int_o^\pi \frac{\lambda r d \theta}{4 \pi \varepsilon_o r^2} \sin \theta(-\hat{j}) \\
& E=-\int_o^\pi \frac{q r \sin \theta d \theta}{4 \pi^2 \varepsilon_o r^3} \hat{j} \\
& =-\frac{q}{4 \pi^2 \varepsilon_o r^2}(-\cos \theta)_o^\pi \hat{j} \\
& \therefore E=-\frac{q}{2 \pi \varepsilon_o r^2} \hat{j}
\end{aligned}
$

Example 5: The intensity of the electric field required to balance a proton of mass $1.7 \times 10^{-27} \mathrm{~kg}$ and charge $1.6 \times 10^{-19} \mathrm{C}$ is nearly
1) $1 \times 10^{-7} \mathrm{~V} / \mathrm{m}$
2) $1 \times 10^{-5} \mathrm{~V} / \mathrm{m}$
3) $1 \times 10^7 \mathrm{~V} / \mathrm{m}$
4) $1 \times 10^5 \mathrm{~V} / \mathrm{m}$
Solution:

Electric Field Intensity

$\vec{E}=\frac{\vec{F}}{q_0}=\frac{k Q}{r^2}$

wherein

Since

$q E=m g$ or $E=\frac{m g}{q}=\frac{1.7 \times 10^{-27} \times 9.8}{1.6 \times 10^{-19}}$

After solving we get Ans A.

Summary

The electric field is a space around a charged particle which causes it to apply forces on other charged bodies. This is shown by lines that begin with positive charges and end with negative charges. Distance from the charge reduces the amount of field present. Understanding how electric forces function is highly dependent on electric fields which in turn influence the manner in which charged objects interact with one another.

Frequently Asked Questions (FAQs)

1. What's the difference between electric field and electric force?
Electric field is a property of space around charged objects, measured in newtons per coulomb (N/C). Electric force is the actual force experienced by a charged particle in an electric field, measured in newtons (N). The electric force depends on both the field strength and the charge of the particle.
2. What is the electric field inside a charged conductor?
The electric field inside a charged conductor in electrostatic equilibrium is always zero. This is because any net field would cause charges to move, contradicting the equilibrium condition. All excess charge in a conductor resides on its surface.
3. How do electric dipoles interact with uniform electric fields?
An electric dipole in a uniform electric field experiences a torque that tries to align it with the field. If the dipole is not aligned, it will rotate. However, there is no net force on the dipole if the field is truly uniform.
4. Can electric fields do work?
Yes, electric fields can do work on charged particles. When a charged particle moves in an electric field, the field exerts a force on the particle, potentially changing its kinetic energy. The work done is equal to the change in the particle's electric potential energy.
5. What is the relationship between charge density and electric field?
For a continuous charge distribution, the electric field at a point is related to the charge density through volume integrals (for volume charge distributions), surface integrals (for surface charge distributions), or line integrals (for line charge distributions). The exact relationship depends on the geometry of the charge distribution.
6. What is an electric field?
An electric field is a region around an electrically charged object where other charged particles experience a force. It's an invisible field that extends through space, representing the electric force per unit charge at any given point.
7. How do conductors and insulators affect electric fields?
Conductors allow charges to move freely, so in electrostatic equilibrium, the electric field inside a conductor is zero, and the field lines are perpendicular to the conductor's surface. Insulators don't allow charge movement, so electric fields can exist within them and field lines can pass through them.
8. What are electric field lines?
Electric field lines are imaginary lines used to visualize electric fields. They start from positive charges and end on negative charges (or extend to infinity). The density of these lines represents the field strength, and their direction at any point shows the direction of the electric field.
9. What is the significance of electric field lines never crossing?
Electric field lines never cross because the electric field has a unique direction at every point in space. If field lines crossed, it would imply that the field has two different directions at the same point, which is physically impossible.
10. How does the electric field behave at the surface of a charged conductor?
At the surface of a charged conductor, the electric field is perpendicular to the surface and its magnitude is proportional to the surface charge density. This is a consequence of Gauss's law and the fact that there can be no tangential component of the field at the surface of a conductor in electrostatic equilibrium.
11. How is the direction of an electric field determined?
The direction of an electric field is defined as the direction of the force experienced by a positive test charge placed in the field. It points away from positive charges and towards negative charges.
12. Can electric fields exist in a vacuum?
Yes, electric fields can exist in a vacuum. Unlike some other types of fields, electric fields don't require a medium to propagate through. They extend through empty space around charged particles.
13. How does the strength of an electric field change with distance from a point charge?
The strength of an electric field decreases with the square of the distance from a point charge. This relationship is known as the inverse square law. If you double the distance, the field strength becomes one-fourth of its original value.
14. What is the superposition principle for electric fields?
The superposition principle states that the total electric field at any point due to multiple charges is the vector sum of the individual fields produced by each charge. This allows us to calculate complex electric fields by breaking them down into simpler components.
15. How is the electric field related to electric potential?
The electric field is the negative gradient of the electric potential. In simpler terms, the electric field points in the direction of decreasing electric potential, and its magnitude is equal to the rate of change of potential with distance.
16. How do electric fields behave in plasmas?
In plasmas, which contain free electrons and ions, electric fields can cause complex collective behaviors. The mobile charges can rearrange to shield out external fields (Debye shielding). Strong fields can also cause further ionization, leading to phenomena like electrical breakdown and plasma oscillations.
17. What is Gauss's law and how does it relate to electric fields?
Gauss's law states that the total electric flux through a closed surface is proportional to the enclosed electric charge. It provides a powerful way to calculate electric fields for symmetric charge distributions by relating the field to the charge causing it.
18. What is meant by the term 'field strength'?
Field strength refers to the magnitude of the electric field at a given point. It's typically measured in newtons per coulomb (N/C) or volts per meter (V/m). A stronger field exerts a greater force on a charged particle placed within it.
19. How do electric fields relate to Coulomb's law?
Coulomb's law describes the force between two point charges, while the electric field is the force per unit charge. The electric field due to a point charge can be derived directly from Coulomb's law by dividing the force by the test charge.
20. How does the concept of electric fields relate to Faraday's idea of 'action at a distance'?
The concept of electric fields, introduced by Michael Faraday, replaced the notion of 'action at a distance' in electromagnetism. It suggests that charges interact by creating a field that permeates space, rather than exerting forces on each other directly across empty space.
21. What happens to the electric field at sharp points on a charged conductor?
The electric field strength becomes very high near sharp points or edges of a charged conductor. This is because charge tends to accumulate at these locations, leading to a high charge density and consequently a strong electric field. This phenomenon is known as the 'lightning rod effect'.
22. How do dielectrics affect electric fields?
Dielectrics weaken the electric field within them. When placed in an electric field, the molecules in a dielectric polarize, creating an internal field that opposes the external field. This reduces the overall field strength within the dielectric material.
23. What is the electric field inside a hollow charged sphere?
The electric field inside a hollow charged sphere is zero, regardless of the charge on the sphere. This is because the charges on opposite sides of the sphere cancel each other's effects at every point inside the sphere.
24. How does the electric field of a finite line charge differ from that of an infinite line charge?
For an infinite line charge, the electric field decreases as 1/r, where r is the perpendicular distance from the line. For a finite line charge, the field behavior is more complex and depends on the position relative to the ends of the line. Near the center and close to the line, it approximates the infinite case, but it falls off more rapidly at larger distances.
25. What is meant by 'electric field flux'?
Electric field flux is a measure of the electric field passing through a given surface. Mathematically, it's the surface integral of the electric field over the area. Conceptually, it's related to the number of field lines passing through the surface.
26. How do electric fields behave in materials with different permittivities?
The electric field in a material is inversely proportional to its permittivity. Materials with higher permittivity (like water) will have weaker internal electric fields compared to materials with lower permittivity (like air) for the same applied external field.
27. What is the relationship between electric field and charge movement?
An electric field exerts a force on charged particles, causing them to accelerate if they're free to move. In conductors, this leads to charge redistribution until the field inside becomes zero. In insulators, it can cause slight shifts in electron positions, leading to polarization.
28. How does the electric field of a point charge compare to that of a charged sphere?
Outside the sphere, the electric field of a uniformly charged sphere is identical to that of a point charge with the same total charge located at the center of the sphere. Inside the sphere, the field increases linearly from zero at the center to its maximum value at the surface.
29. What is the significance of equipotential surfaces in relation to electric fields?
Equipotential surfaces are surfaces where the electric potential is constant. Electric field lines are always perpendicular to equipotential surfaces. This relationship helps in visualizing and understanding the three-dimensional nature of electric fields.
30. How do electric fields behave at the atomic level?
At the atomic level, electric fields are extremely strong due to the small distances involved. The electric field near an atomic nucleus can be on the order of 10^11 N/C. These strong fields are responsible for holding electrons in their orbitals and play a crucial role in chemical bonding.
31. What is the principle behind Faraday cages and how does it relate to electric fields?
A Faraday cage is a conductive enclosure that blocks external electric fields. It works because the charges in the conductive material redistribute themselves to cancel the external field inside the cage. This principle is based on the fact that the electric field inside a conductor in electrostatic equilibrium is zero.
32. How does the electric field of a dipole differ from that of a single charge?
The electric field of a dipole falls off more rapidly with distance compared to a single charge. For a dipole, the field decreases as 1/r^3 at large distances, where r is the distance from the dipole center. For a single charge, it decreases as 1/r^2.
33. What is the significance of the electric field in capacitors?
In a capacitor, the electric field stores energy. The field exists in the space between the plates and is approximately uniform for parallel plate capacitors. The capacitance is directly related to the electric field strength and the geometry of the capacitor.
34. How do electric fields relate to the concept of electric potential energy?
Electric potential energy is the energy a charged particle has due to its position in an electric field. The change in potential energy when moving a charge in an electric field is equal to the negative of the work done by the field on the charge.
35. What is meant by the term 'electric field screening'?
Electric field screening refers to the reduction of an electric field's strength due to the presence of other charges. For example, in a plasma or an electrolyte solution, mobile charges arrange themselves to partially cancel out external electric fields, effectively 'screening' the field.
36. How does the electric field behave near the edge of a charged conducting plate?
Near the edge of a charged conducting plate, the electric field becomes stronger and its direction changes. This is because charge tends to accumulate at edges and corners, leading to a higher charge density. The field lines near the edge are no longer parallel but curve outward.
37. What is the relationship between electric field and charge acceleration in a vacuum?
In a vacuum, a charged particle in an electric field experiences an acceleration directly proportional to the field strength and inversely proportional to its mass. The direction of acceleration is the same as the field direction for positive charges and opposite for negative charges.
38. How do electric fields contribute to the phenomenon of lightning?
Lightning occurs when there's a large buildup of electric charge in clouds, creating strong electric fields. When the field strength exceeds the breakdown strength of air (about 3 million V/m), it ionizes the air, creating a conductive path for a rapid discharge of electricity - lightning.
39. What is the principle behind the Van de Graaff generator and how does it relate to electric fields?
The Van de Graaff generator creates high electric potentials by continuously transferring charge to a hollow metal sphere. It utilizes the principle that in a conductor, excess charge resides on the outer surface. The strong electric field near the sphere's surface can be used to demonstrate various electrostatic phenomena.
40. How do electric fields behave in semiconductors?
In semiconductors, electric fields can cause the movement of both electrons and holes (electron vacancies). The behavior is more complex than in simple conductors or insulators, as the field can influence the concentration of charge carriers and their mobility, leading to various important electronic effects.
41. What is the connection between electric fields and electromagnetic waves?
Electromagnetic waves, including light, consist of oscillating electric and magnetic fields perpendicular to each other and to the direction of wave propagation. The electric field component of these waves can interact with charged particles, allowing the wave to transfer energy and momentum.
42. How does the concept of electric field relate to Coulomb's law?
Coulomb's law describes the force between two point charges, while the electric field is defined as the force per unit charge. The electric field due to a point charge can be derived directly from Coulomb's law by dividing the force expression by the test charge.
43. What is the significance of Gauss's law in calculating electric fields?
Gauss's law provides a powerful method for calculating electric fields, especially for symmetric charge distributions. It relates the flux of the electric field through a closed surface to the enclosed charge, often simplifying calculations that would be complex using Coulomb's law directly.
44. How do electric fields behave in anisotropic materials?
In anisotropic materials, the electric field's behavior depends on its direction relative to the material's structure. The electric displacement field may not be parallel to the electric field, and the material's response to the field can vary along different axes.
45. What is the relationship between electric field and current in Ohm's law?
Ohm's law relates current density to electric field in a conductor. In its microscopic form, it states that the current density is proportional to the electric field, with the conductivity as the proportionality constant. This relationship holds for many materials but not for all.
46. How do electric fields contribute to the functioning of particle accelerators?
Particle accelerators use strong electric fields to accelerate charged particles to high speeds. The fields are often created by radio-frequency cavities and can be synchronized to provide continuous acceleration. The particles gain kinetic energy from the work done by these fields.
47. What is the principle of electrostatic shielding and how does it relate to electric fields?
Electrostatic shielding involves using a conducting enclosure to protect an area from external electric fields. It works because the charges in the conductor redistribute to cancel the external field inside the enclosure. This principle is used in various applications, from sensitive electronic equipment to cable shielding.
48. What is the connection between electric fields and the photoelectric effect?
In the photoelectric effect, light incident on a material causes electron emission. The electric field component of the light provides the energy to liberate electrons. Additionally, an external electric field is often applied to collect the emitted electrons, influencing their motion after emission.
49. How do electric fields relate to the concept of electrical breakdown in insulators?
Electrical breakdown occurs when the electric field in an insulator becomes strong enough to accelerate free electrons to energies sufficient to ionize atoms through collisions. This creates more free electrons, leading to an avalanche effect and sudden increase in conductivity. The field strength at which this occurs is called the dielectric strength of the material.
50. What is the significance of electric fields in the operation of field-effect transistors (FETs)?
In field-effect transistors, an electric field controls the flow of current through a semiconductor channel. The field is created by applying a voltage to the gate electrode, which modulates the conductivity of the channel. This principle allows FETs to amplify or switch electronic signals, forming the basis of modern digital electronics.

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