Electrostatics for JEE Main 2025: Key Concepts and Applications

Name of the Concept

Key Points of the Concept

1. Electric Charges: Conservation of Charge

• Electric charge, also known as charge or electrostatic charge, is defined as the basic property of subatomic particles that causes them to experience a force when placed in an electromagnetic field. In general, electric charges are of two types – positive carried by the charge carriers named protons and negative by charge carriers termed as electrons. If the net charge of an object is equal to zero, i.e. neither positive nor negative, then it is said to be neutral. Electric charge is symbolized as Q and measured using a coulomb.  

• S.I Unit of Charge is Coulomb. 

• Positively Charged Particles:

In this type of particle, numbers of positive ions (protons) are larger than the numbers of negative ions (electrons). To neutralize positively charged particles, electrons from the surroundings come to this particle until the number of protons and electrons become equal.

• Negatively Charged Particles:

Similarly, electrons are larger in number than that of protons. To neutralize negatively charged particles, electrons move to the ground or any other particle around until the number of protons and electrons become equal. 

2. Coulomb’s Law

• Coulomb’s law gives us the magnitude of the force acting between two charges placed at a distance. Coulomb's law defines the magnitude of electrostatic force acting between point charges.

• Coulomb’s law states that force acting between two charges is directly proportional to the product of the magnitude of charges and inversely proportional to the square of the distance between them.

$F\propto\dfrac{q_1q_2}{r^2}$

$F=k\dfrac{q_1q_2}{r^2}$

Where q1 and q2 are the two charges placed at a distance r between them.

$k=\dfrac{1}{4\pi\epsilon}$

• K is the Coulomb’s constant and ε is the permittivity of the medium and the value of permittivity of vacuum is 8.85 × 10-12 Nm2/kg2

3. Coulomb’s First Law

• Bodies with like charges repel each other, and bodies with unlike (opposite) charges, attract each other.

4. Coulomb’s Second Law

• The force, whether of attraction or repulsion, between two charged bodies is directly proportional to the product of their charges and inversely to the square of the distance amid them. 

• According to the second law, 

F ∝ Q1 Q2 and F ∝ 1/d2

Hence, F ∝ ((Q1 Q2) / d2)

F = k ((Q1/Q2)/d2)

Where,

Q1 and Q2 = Charges of the charged bodies

d = distance amid the centre of the two charged bodies

k = constant based on the medium in which the bodies are positioned

F = Force of attraction or repulsion between the charged bodies

Note: Both the S.I and M.K.S system, k = 1/4 εoεr and the value of εo =8.854 x 10⁻¹² C²/Nm². The value of εr that changes with change in medium is 1 in vacuum and air.

5. Principle of Coulomb's Law

• To understand the principle of Coulomb's Law, suppose you have two bodies, out of which one is positively charged, and the other is negatively charged. In this case, the two bodies will attract each other as they have opposite charges. Now, if you increase the charge of one body, leaving the other one as it is, then the force of attraction will increase. Hence, we can conclude that the force amid the charged bodies is directly proportional to the charge of the bodies. Now, keeping the charge Q1 and Q2 of the two bodies constant, if you bring them closer, the force amid them will increase. However, if you place them far from each other, then the force will decrease. So, we can say that the force between two charged bodies is inversely proportional to the distance between them. 

• Remember that the force developed between two charged bodies isn't the same in all the mediums, and vary with the mediums.

6. Electric field and electric lines of force

• Electric field intensity (E) at a point is the electrostatic force acting on a unit test charge placed in the electric field.

$E=\dfrac{F}{q}$

$E=\dfrac{1}{4\pi\epsilon}\dfrac{q_1q_2}{r^2}$

• Electric lines of force are the lines that represent the electric field at that point.

• Electric field lines never intersect each other and the tangent to the electric field lines at a point gives the direction of the electric field at that point.

7. Electric field due to continuous charge distribution

• Electric field due to infinitely long charged wire having linear charge density 𝜆 at a distance r is 

$E=\dfrac{1}{4\pi\epsilon}\dfrac{2\lambda}{r}$

•  Electric field due to a uniformly charged  disc having radius R and surface charge density 𝜎 along its axis is

$E=\dfrac{\sigma}{2\pi\epsilon_0}\left(1-\dfrac{z}{\sqrt{z^2+r^2}}\right)$

• Electric field due to a charged infinite thin plane sheet having surface density 𝜎

$E=\dfrac{\sigma}{2\pi\epsilon_0}$

8. Electric dipole and dipole moment

• Electric dipole is a pair of equal and opposite charges separated by a small distance.

• Magnetic dipole moment (P) is the product of the magnitude of one charge(q) and the distance between them(d). 

$\vec P=q\times \vec d$

• It is a vector quantity and its direction is from negative charge to positive charge.

• Torque experienced by a dipole in a uniform electric field is 

$\vec\tau=\vec P\times \vec E$

• Potential energy of dipole in a uniform electric field is 

$U=-\vec P\cdot \vec E$

$U=-P E\cos\theta$

9. Torque on a Dipole in a Uniform Electric Field

• When an electric dipole is placed in a uniform electric field, it experiences a torque. The torque is calculated using the formula:

• τ = p * E * sin(θ)

Where 

τ is the torque

p is the dipole moment

E is the electric field strength, 

θ is the angle between the dipole moment and the electric field. 

10. Electric Flux

• Electric flux is a fundamental concept in electrostatics that measures the flow of electric field lines through a given surface. It is denoted by the symbol Φ (phi) and is defined as the dot product of the electric field (E) and the surface area vector (A) over a closed surface:

Φ = ∫∫E · dA

• In simpler terms, electric flux quantifies the number of electric field lines passing through a particular area. It can be positive, negative, or zero depending on the orientation of the electric field and the surface.

11. Gauss Law

• According to Gauss Law, the net flux linked with a closed surface is equal to 1/ε0 times the net charge enclosed inside the surface.

$\oint\vec E\cdot d\vec s=\dfrac{q_{enclosed}}{\epsilon_0}$

12. Electric potential and Equipotential surface

• Electric potential at a point is the amount of work done (W) in bringing a unit positive charge from infinity to that point along any arbitrary path. It is a scalar quantity.

$V=\dfrac{W}{q}$

• Electric potential due to a point charge (q) at a distance r is

$V=\dfrac{1}{4\pi\epsilon_0}\dfrac{q}{r}$

• Electric potential energy of two charge systems at a distance r between them is

$U=\dfrac{1}{4\pi\epsilon_0}\dfrac{q_1q_2}{r}$ 

• In an equipotential surface, every point has the same potential.

Example: Surface of a charged surface

13. Electric potential due to various charge distribution

• Electric potential due to a charged ring of radius R along its axis at a distance x from its centre

$V=\dfrac{1}{4\pi\epsilon_0}\left(\dfrac{Q}{\sqrt{x^2+R^2}}\right)$

• Electric potential due to a charged sphere having radius R and charge Q

At any point Inside the sphere: 

$V=\dfrac{1}{4\pi\epsilon_0}\dfrac{Q}{R}$

On the surface of the sphere:

$V=\dfrac{1}{4\pi\epsilon_0}\dfrac{Q}{R}$

At a point outside the sphere at a distance r from the centre of the sphere.

$V=\dfrac{1}{4\pi\epsilon_0}\dfrac{Q}{r}$

14. Conductors and Insulators

• In the world of electrostatics, materials can be broadly classified into two categories: conductors and insulators. Conductors are materials that allow electric charges to move freely within them. This is due to the presence of loosely bound electrons that can easily migrate in response to an applied electric field. Metals like copper and aluminum are excellent examples of conductors.

• On the other hand, insulators are materials that do not allow the free movement of electric charges. In insulators, electrons are tightly bound to their atomic nuclei, making it difficult for them to move. Materials like rubber, plastic, and glass are common insulators.

15. Dielectrics and Electric Polarization

• Dielectrics are a type of insulator that play a crucial role in the field of capacitors. When a dielectric material is placed between the plates of a capacitor, it becomes electrically polarized. This means that the electric charges within the dielectric material shift slightly in response to the electric field, creating temporary dipoles. This polarization helps to increase the capacitance of the capacitor and can store more electric charge.

16. Capacitance of a capacitor

• The ability to store charge is called capacitance. Its unit is farad. The capacitance of a capacitor is given by

$C=\dfrac{Q}{V}$

• Capacitance of parallel plate capacitor having area A and distance between the plate d is

$C=\dfrac{kA\epsilon_0}{d}$

• Increase in dielectric constant (k) of a dielectric medium increases the capacitance.

17. Grouping of Capacitance

• Capacitors in series:

The charge stored in capacitors in series combination is the same but the potential difference across each capacitor is different.

$\dfrac{1}{c_{eq}}=\dfrac{1}{c_1}+\dfrac{1}{c_2}+\dfrac{1}{c_3}$

• Capacitors in parallel

The potential across each capacitor in parallel is the same and the charge will be different.

$c_{eq}=c_{1}+c_{2}+c_{3}$

18. Capacitance of a Parallel Plate Capacitor with and without Dielectric Medium

• The capacitance of a parallel plate capacitor can be calculated using the formula 

C = ε₀ * (A / d)

Where,

C is the capacitance

ε₀ is the vacuum permittivity

A is the area of the plates

d is the separation between the plates. 

• When a dielectric material is introduced between the plates, the capacitance increases by a factor equal to the material's relative permittivity (k). This can be expressed as C = k * ε₀ * (A / d).

Sl. No

Name of the Concept

Formula

1.

Relation between electric field and electric potential

• $\vec E=\dfrac{\partial V}{\partial x} \hat i+\dfrac{\partial V}{\partial y} \hat j+\dfrac{\partial V}{\partial z} \hat k$

• $\vec E=E_x \hat i+E_y \hat j+E_z \hat k $

• $V=\int_{x_1}^{x_2} E_x +\int_{y_1}^{y_2} E_y +\int_{z_1}^{z_2} E_z  $

2.

Electric field due to a charged conducting sphere having charge (Q) and radius R

• At a point inside the sphere,

$E_{inside}=0$

• At a point on the surface of the sphere,

$E=\dfrac{1}{4\pi\epsilon_0}\dfrac{Q}{R^2}$

• At a point outside the sphere at a distance r from the centre of the sphere,

$E=\dfrac{1}{4\pi\epsilon_0}\dfrac{Q}{r^2}$

3.

Electric field due to a charged non-conducting sphere having volume  charge density (⍴) and radius R

• At a point inside the sphere and at a distance r from the centre

$E=\dfrac{\rho r}{3\epsilon_0}$

• At a point on the surface of the sphere

$E=\dfrac{\rho R}{3\epsilon_0}$

• At a point outside the sphere and at a distance r from the centre of the sphere

$E=\dfrac{\rho R^3}{3\epsilon_0r^2}$

4.

Electric field due to a dipole having dipole moment P

• Electric field due to a dipole at an axial point at a distance r from its centre

$E=\dfrac{1}{4\pi\epsilon_0}\dfrac{2P}{r^3}$

• Electric field due to a dipole at an equatorial point at a distance r from its centre

$E=\dfrac{1}{4\pi\epsilon_0}\dfrac{P}{r^3}$

5.

Electric potential due to a dipole

• Electric potential due to a dipole having dipole moment (P) at a distance r from the centre is

$V=\dfrac{1}{4\pi\epsilon_0}\dfrac{P\cos(\theta)}{r^2}$ 

6.

Energy stored in a capacitor

$U=\dfrac{1}{2}CV^2$

$U=\dfrac{1}{2}QV$

$U=\dfrac{Q^2}{2C}$

Where Q is the charge stored, V is the potential difference and C is the capacitance.

7.

Energy density of a capacitor

$E.D=\dfrac{1}{2}\varepsilon_0E^2$

Where E is the electric field.

8.

Work done in rotating a dipole in an electric field from θ1 to θ2

$W=PE(\cos\theta_1-\theta_2)$

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