Mathematical definition
E = F / q₀
- E is electric field intensity.
- F is the force experienced by the test charge.
- q₀ is a small positive test charge.
- Unit: N/C or V/m.
- Direction: direction of force on a positive test charge.
Class 12 Electrostatics Masterclass
Electric Field Concept
Electric field is the invisible influence created around a charge. It tells us how strongly and in what direction another charge would experience electric force at any point in space.
- CBSE Class 12
- NEET
- JEE Main
- JEE Advanced
- IB Physics
- ICSE
- IGCSE
- British Curriculum
Section 1
Definition of Electric Field
Electric field at a point is defined as the force experienced per unit positive test charge placed at that point.
Physical meaning
A source charge modifies the space around it. If a tiny positive charge is brought to a point, it experiences force because that point already has an electric field. The test charge is kept very small so that it measures the field without disturbing the source charge distribution.
Electric field is a vector quantity. A large magnitude of E means a strong force per coulomb; direction tells where a positive charge would be pushed.
Section 2
Electric Field Due to a Point Charge
The electric field due to a point charge is obtained directly from Coulomb's law by dividing force by the positive test charge.
NCERT-style derivation
Let a source charge Q be placed at a point. A small positive test charge q₀ is placed at distance r from Q.
By Coulomb's law, the force on q₀ is
F = (1 / 4πε₀) × (Qq₀ / r²)
Electric field is force per unit positive test charge:
E = F / q₀
Substituting F and cancelling q₀ gives
E = (1 / 4πε₀) × (Q / r²)
Key interpretation
- Field is radially outward for a positive charge.
- Field is radially inward for a negative charge.
- Electric field decreases as inverse square of distance.
- Electric field is a vector, so superposition must include direction.
- The formula gives magnitude; sign or diagram gives direction.
E ∝ 1 / r²
Section 3
Electric Field Lines
Field lines are imaginary curves drawn so that the tangent at any point gives the direction of electric field. Their spacing represents field strength.
Field lines due to +Q
Field lines due to -Q
Two positive charges
+Q and -Q pair
Two negative charges
Section 4
Significance of Electric Field
Electric field gives a powerful way to understand action at a distance without imagining that one charge directly pulls another through empty space.
Field as property of space
A charge creates electric field in surrounding space. Another charge placed there interacts with the field and experiences force.
Foundation of electrostatics
Electric field helps explain force, potential, capacitance, dipoles, conductors, dielectrics and Gauss law.
Exam importance
For CBSE, NEET and JEE, electric field is the bridge between charge-force problems and advanced electrostatics.
Section 5
Properties of Electric Field Lines
- Electric field lines start from positive charge and end on negative charge.
- For an isolated positive charge, lines go to infinity.
- For an isolated negative charge, lines come from infinity and terminate on the charge.
- Tangent to a field line gives direction of electric field.
- Field lines never intersect.
- Crowding of field lines represents stronger electric field.
- Field lines are perpendicular to conductor surface in electrostatic equilibrium.
- No electric field lines exist inside an electrostatic conductor.
- Field lines do not form closed loops in electrostatics.
- Field lines are imaginary but represent real field direction and strength.
Section 6
Electric Dipole
An electric dipole consists of two equal and opposite charges +q and -q separated by a small distance 2a.
Dipole moment
p = q × 2a
- Direction of dipole moment is from -q to +q.
- SI unit of dipole moment is C m.
- Dipoles are important in molecular physics, dielectric polarization, torque in electric field and electrostatic potential.
Electric dipole diagram
Section 7
Electric Field Intensity at an Axial Point Due to a Dipole
NCERT-style derivation
Place -q at A and +q at B, separated by 2a. Let O be the centre and P be an axial point at distance r from O.
Distance from +q to P is r - a and distance from -q to P is r + a.
Field at P due to +q is along OP, and field due to -q is opposite. Net field is
E = (1 / 4πε₀) q[1/(r - a)² - 1/(r + a)²]
Simplifying gives
E_axial = (1 / 4πε₀) × [2pr / (r² - a²)²]
For a short dipole, r >> a, so
E_axial = (1 / 4πε₀) × (2p / r³)
Axial point diagram
Direction
At an axial point on the side of +q, the net field is along the dipole moment. On the opposite side, the direction remains along the axial line according to vector subtraction of the two fields.
Section 8
Electric Field Intensity at an Equatorial Point Due to a Dipole
Equatorial point diagram
NCERT-style derivation
Let P be on the perpendicular bisector of the dipole at distance r from centre O.
Distance from P to each charge is √(r² + a²). The vertical components of the two fields cancel.
Horizontal components add opposite to dipole moment.
The magnitude becomes
E_equatorial = (1 / 4πε₀) × [p / (r² + a²)^(3/2)]
For a short dipole, r >> a, so
E_equatorial = (1 / 4πε₀) × (p / r³)
Section 9
Comparison of Axial and Equatorial Electric Field
| Point of comparison | Axial point | Equatorial point |
|---|---|---|
| Position of point | On the line joining -q and +q | On the perpendicular bisector of the dipole |
| Magnitude | (1 / 4πε₀) × [2pr / (r² - a²)²] | (1 / 4πε₀) × [p / (r² + a²)^(3/2)] |
| Direction | Along dipole axis; commonly along p on the +q side | Opposite to dipole moment |
| Short dipole formula | (1 / 4πε₀) × 2p / r³ | (1 / 4πε₀) × p / r³ |
| NEET importance | Direct formula and direction questions are common | Frequently tests the “opposite to p” direction trap |
| JEE importance | Used in superposition and limiting approximation | Used in vector cancellation and component-based reasoning |
Section 10
Electric Field Due to a Moving Charge
Class 12 level view
In electrostatics, we mainly study electric field due to charges at rest. The field due to stationary point charges, systems of charges and dipoles forms the foundation of CBSE, NEET and JEE electrostatics.
A moving charge produces both electric field and magnetic field. At non-relativistic school level, the electric field concept is usually introduced using stationary point charges.
Important correction
Use the term moving charge or charge in motion. Do not write “current-carrying charge” as a standard term. Advanced treatment of fields due to moving charges belongs to electromagnetism and relativity.
Section 11
Important Formulas
E = F / q₀Definition of electric field intensity.
E = (1 / 4πε₀) × Q / r²Field due to a point charge.
p = q × 2aElectric dipole moment.
E_axial = (1 / 4πε₀) × 2p / r³Short dipole axial field.
E_equatorial = (1 / 4πε₀) × p / r³Short dipole equatorial field.
F = qEForce on charge q in electric field E.
+Q: outwardField direction due to positive charge.
-Q: inwardField direction due to negative charge.
Section 12
Common Mistakes by Students
Source vs test charge
The source charge creates the field. The test charge measures it. Do not mix Q and q₀.
Wrong direction
Field is outward for positive source charge and inward for negative source charge.
Ignoring vector nature
Electric field has magnitude and direction; superposition must be vector addition.
Axial-equatorial confusion
Axial short dipole field has 2p/r³, equatorial has p/r³.
Equatorial direction trap
Equatorial field is opposite to dipole moment.
Wrong dipole distance
Use distance from centre O carefully: axial distances to charges are r - a and r + a.
Intersecting field lines
Field lines never intersect because electric field cannot have two directions at one point.
Field lines as wires
Field lines are imaginary representation, not real physical threads or wires.
Section 13
NCERT Style Summary
Electric field at a point is the force per unit positive test charge placed at that point, E = F/q₀. It is a vector quantity and its direction is the direction of force on a positive test charge. A point charge Q produces an electric field E = (1/4πε₀)Q/r², directed radially outward for positive charge and radially inward for negative charge. Electric field lines help visualize direction and relative strength of electric field; they start from positive charges and end on negative charges, never intersect, and are closer where the field is stronger. An electric dipole consists of charges +q and -q separated by distance 2a, with dipole moment p = q × 2a directed from -q to +q. For a short dipole, axial field is (1/4πε₀)2p/r³ and equatorial field is (1/4πε₀)p/r³ opposite to p.
Section 14
Question Bank
Original exam-pattern questions with answers and short explanations. These are arranged by curriculum and difficulty, and they intentionally test different concepts instead of repeating the same numerical pattern.
Section 15
Case Study Questions
Each case study contains a short context and 4-5 linked questions with answers.
Section 16
Why Learn Electric Field Properly?
Electric potential
Potential is built from electric field and work done per unit charge.
Capacitance
Capacitors store energy in electric fields between conductors.
Gauss law
Field symmetry is the key to applying Gauss law correctly.
Current electricity
Electric field inside conductors drives drift of charges.
Dielectrics
Polarization of dielectrics depends on dipoles responding to electric field.
Modern technology
Sensors, capacitive touchscreens, electronics and electromagnetic devices all use field concepts.
Need Help Understanding Electric Field?
If you are facing difficulty in electric field, electric field lines, dipole, axial field, equatorial field or NEET/JEE numerical questions, contact Kumar Sir for one-to-one online Physics classes.
Date: 20-Dec-2025
Electrostatics: Electric Field Study Notes
1. Electric Field & Intensity
The space around a charge where its influence is felt is the Electric Field.
Intensity ($\vec{E}$): Force per unit test charge.
$$\vec{E} = \frac{\vec{F}}{q_0}$$
📝 Doodle: Draw a small sun-like charge with rays going out!
2. Field due to Point Charge
For a charge $Q$ at distance $r$, the field is:
$$E = \frac{1}{4\pi\epsilon_0} \frac{Q}{r^2}$$
3. Group of Charges (Superposition)
Net field is the Vector Sum of all individual fields.
$\vec{E}_{net} = \vec{E}_1 + \vec{E}_2 + … + \vec{E}_n$
4. Continuous Charge Distribution
When charges are spread over a line, surface, or volume:
- Linear ($\lambda$): $dq = \lambda dl$
- Surface ($\sigma$): $dq = \sigma dS$
- Volume ($\rho$): $dq = \rho dV$
$$E = \int \frac{1}{4\pi\epsilon_0} \frac{dq}{r^2} \hat{r}$$
5. Rectangular Components
Resolving $\vec{E}$ into $E_x, E_y, E_z$ components:
$\vec{E} = E_x\hat{i} + E_y\hat{j} + E_z\hat{k}$
Where $E_x = \frac{1}{4\pi\epsilon_0} \frac{qx}{r^3}$ etc. 📐 (Triangle Doodle)
6. Physical Significance
It helps us understand how Forces are transmitted through space even without contact. It defines the electrical environment around a charge.
7. Electric Field Lines
Imaginary smooth curves representing the field direction.
Top 3 Properties:
- Start from $(+)$ and end at $(-)$.
- Tangent gives Direction of $\vec{E}$.
- Two lines NEVER intersect. ❌
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✏️ Note: $E \sin \theta$ components cancel each other!
Field Intensity on Equatorial Line ⚡
Consider an electric dipole with charges -q and +q separated by 2a. We calculate electric field $E$ at point P on the equatorial line at distance r.
-q+qOaaPrE₁E₂E_net
Step 1: Magnitude of fields $E_1$ and $E_2$ are equal:
$$|E_1| = |E_2| = \frac{1}{4\pi\epsilon_0} \frac{q}{(r^2 + a^2)}$$
Step 2: Resultant intensity $E$ is the sum of cosine components:
$E = 2E_1 \cos \theta$
Substituting $\cos \theta = \frac{a}{(r^2 + a^2)^{1/2}}$:
$$\vec{E}_{equatorial} = \frac{1}{4\pi\epsilon_0} \frac{\vec{p}}{(r^2 + a^2)^{3/2}}$$
For a Short Dipole ($r >> a$), the formula becomes:
$E = \frac{1}{4\pi\epsilon_0} \frac{p}{r^3}$
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