Electric Field – Class 12 + JEE Main | Complete Notes
Electric Field Electrostatics ka one of the most important concepts hai. Class 12 Physics mein is topic se direct formula-based questions ke saath-saath vector addition, superposition principle, electric field lines, continuous charge distribution aur conductor-based questions bhi pooche jaate hain.
JEE Main ke liye sabse important baat hai ki aap sirf formula yaad na karein, balki field ki magnitude + direction + distance dependence ko clearly understand karein.
Is complete article mein hum electric field ki definition se lekar point charge, multiple charges, field lines, continuous charge distribution, infinite line charge, infinite sheet, conductor aur JEE Main shortcut tak sab kuch step-by-step cover karenge.
1. What is Electric Field? ⭐
Electric field ko simply samajhne ke liye socho ki ek charged body apne surroundings mein ek effect create karti hai. Agar hum us region mein ek small positive test charge place karein, to us charge par electric force act karega.
Electric Field = Force experienced by unit positive test charge.
Mathematically:
E = F / q₀
Yahan:
- E = Electric field
- F = Force experienced by test charge
- q₀ = Small positive test charge
SI Unit
SI Unit of Electric Field = N/C
Electric field ek vector quantity hai, isliye iski magnitude ke saath direction bhi hoti hai.
Direction of Electric Field
Electric field ki direction woh direction hai jisme ek positive test charge force experience karega.
Important: Field ki direction define karne ke liye positive test charge consider kiya jata hai.
2. Electric Field Due to a Point Charge ⭐
Suppose ek point charge Q hai aur usse distance r par electric field find karna hai.
Point charge ke due to electric field:
E = kQ/r²
where:
k = 1/(4πε₀)
Vacuum mein:
k ≈ 9 × 10⁹ N·m²/C²
Dependence of Electric Field
Formula:
E = kQ/r²
Isse directly:
E ∝ Q
aur:
E ∝ 1/r²
Therefore, charge double hone par field double hota hai, lekin distance double hone par field four times decrease hota hai.
Direction
Positive charge (+Q) → Field away from charge
Negative charge (−Q) → Field towards charge
Ye direction JEE Main ke vector questions mein extremely important hai.
3. Electric Field and Electric Force
Agar kisi electric field E mein ek charge q place kiya jaye, to us charge par electric force:
F = qE
Is relation ko electric field ki definition se bhi samjha ja sakta hai:
E = F/q
Therefore:
F = qE
Direction of Force
q > 0 → Force is along E
q < 0 → Force is opposite to E
Yahan ek common confusion hota hai:
Electric field ki direction hamesha positive test charge ke force ki direction hoti hai.
Agar actual charge negative hai, to us par force field ke opposite direction mein hoga.
4. Superposition Principle 🔥
Agar space mein multiple charges present hain, to kisi point par total electric field har individual charge ke electric fields ka vector sum hota hai.
For example, three charges ke liye:
Enet = E₁ + E₂ + E₃
General form:
Enet = ΣE
Sabse important word hai vectorially.
Electric fields ko blindly algebraically add nahi karna chahiye. Pehle direction determine karo.
Same Direction
Agar E₁ aur E₂ same direction mein hain:
Enet = E₁ + E₂
Opposite Direction
Agar dono opposite directions mein hain:
Enet = |E₁ − E₂|
JEE Shortcut
Step 1 → Har charge ka field magnitude find karo.
Step 2 → Har field ki direction determine karo.
Step 3 → Same direction fields ko add karo.
Step 4 → Opposite direction fields ko subtract karo.
Vector nature ko ignore karna superposition questions mein sabse common mistake hai.
5. Two Equal Charges
Two equal charges ke questions JEE Main mein symmetry ke concept ko test kar sakte hain.
Case 1 → +Q and +Q
Do equal positive charges ko ek line par consider karo. Midpoint par dono charges se distance same hoga.
First charge ka field midpoint par ek direction mein hoga, while second charge ka field opposite direction mein hoga.
Magnitudes equal hone ke karan:
Enet = 0
Reason → Equal fields + opposite directions.
Case 2 → +Q and −Q
Ab agar charges equal magnitude ke but opposite signs ke hain, midpoint par electric fields same direction mein hote hain.
Agar midpoint se each charge ki distance r hai:
Each field:
E = kQ/r²
Total:
Enet = 2kQ/r²
Isliye equal opposite charges ke midpoint par field zero nahi hota.
6. Electric Field Lines 🔥
Electric field lines imaginary lines hoti hain jo electric field ki direction aur relative strength ko represent karti hain.
Important Properties
→ Field lines start from positive charge.
→ Field lines end on negative charge.
→ Kisi point par field line ki tangent electric field ki direction batati hai.
→ Electric field lines kabhi intersect nahi karti.
→ More crowded field lines → Stronger field.
→ Less crowded field lines → Weaker field.
→ Electrostatic field lines closed loops form nahi karti.
Why Field Lines Cannot Intersect?
Agar do field lines intersect karengi, to intersection point par electric field ki do different directions ho jayengi. Ek point par electric field ki direction unique hoti hai. Therefore, field lines cannot intersect.
Electric Field Inside an Electrostatic Conductor
Electrostatic equilibrium mein conductor ke inside:
E = 0
Ye conductor-based JEE questions ka fundamental result hai.
7. Electric Field Due to Continuous Charge Distribution
Ab tak humne point charges consider kiye. Lekin practical situations mein charge ek continuous distribution ke form mein bhi ho sakta hai.
Continuous charge distribution ko small elements mein divide kar sakte hain.
Small charge element:
dq
Is small charge element ke due to small electric field:
dE = k dq/r²
Entire charge distribution ka total field integration se obtain hota hai:
E = ∫dE
Charge Densities
Linear Charge Density
Agar charge length par distributed hai:
λ = Q/L
Unit generally C/m.
Surface Charge Density
Agar charge surface par distributed hai:
σ = Q/A
Unit generally C/m².
Volume Charge Density
Agar charge volume mein distributed hai:
ρ = Q/V
Unit generally C/m³.
| Distribution | Density | Formula |
|---|---|---|
| Linear | λ | Q/L |
| Surface | σ | Q/A |
| Volume | ρ | Q/V |
8. Important JEE Results 🔥
Infinite Line Charge
Infinite line charge ke due to electric field:
E = λ/(2πε₀r)
Therefore:
E ∝ 1/r
Notice that point charge ke case mein field 1/r² ke according vary karta tha, whereas infinite line charge ke case mein:
E ∝ 1/r
Infinite Plane Sheet
Uniformly charged infinite plane sheet ke due to field:
E = σ/(2ε₀)
Yahan ek very important observation hai:
Electric field distance par depend nahi karta.
Matlab sheet se distance increase karne par ideal infinite sheet ka electric field magnitude change nahi hota.
9. Two Oppositely Charged Infinite Sheets
Agar do oppositely charged infinite sheets present hain, to unke fields superposition principle ke according add/subtract honge.
Between the Sheets
Between sheets, fields same direction mein hote hain:
E = σ/ε₀
Outside the Sheets
Outside region mein fields cancel ho jaate hain:
E = 0
JEE questions mein direction diagram banakar field addition karna fastest approach hota hai.
10. Electric Field Near a Conductor ⭐
Electrostatic equilibrium mein conductor ke behaviour ke kuch very important results hain.
Inside the Conductor
E = 0
Electrostatic equilibrium mein conductor ke andar electric field zero hota hai.
Just Outside the Conductor
Surface ke just outside electric field:
E = σ/ε₀
Direction
Conductor surface ke just outside electric field:
Surface ke perpendicular hota hai.
Agar electric field mein tangential component hota, to free charges conductor surface par move karte. Electrostatic equilibrium mein aisa nahi hota.
11. JEE Shortcut – Change in Electric Field 🔥
Point charge ke liye:
E = kQ/r²
Isliye quick ratio method use kar sakte ho.
Case 1 → Q Becomes 2Q
E ∝ Q
Therefore:
E′ = 2E
Case 2 → r Becomes 2r
E ∝ 1/r²
Therefore:
E′ = E/4
Case 3 → Q Becomes 2Q and r Becomes 2r
New field:
E′ = k(2Q)/(2r)²
E′ = 2kQ/4r²
Therefore:
E′ = E/2
Golden Rule
E ∝ Q/r²
JEE Main ke ratio-based questions mein is relation se calculation bahut fast ho sakti hai.
12. JEE Main-Level Solved Question 🔥
Question
A point charge Q = 4 μC is placed in vacuum. Find the electric field at a distance of 20 cm from the charge.
Given
Q = 4 μC = 4 × 10⁻⁶ C
r = 20 cm = 0.2 m
k = 9 × 10⁹ N·m²/C²
Formula
E = kQ/r²
Substitution
E = (9 × 10⁹ × 4 × 10⁻⁶)/(0.2)²
Since:
(0.2)² = 0.04
Therefore:
E = 9 × 10⁵ N/C
Answer
Electric Field = 9 × 10⁵ N/C ✅
Since the charge is positive, field ki direction charge se away hogi.
13. Important Comparison for JEE Main
| Source | Electric Field | Distance Dependence |
|---|---|---|
| Point Charge | E = kQ/r² | 1/r² |
| Infinite Line Charge | E = λ/(2πε₀r) | 1/r |
| Infinite Plane Sheet | E = σ/(2ε₀) | Independent of r |
| Conductor – Inside | E = 0 | Not applicable |
| Conductor – Just Outside | E = σ/ε₀ | Surface result |
Ye table direct revision ke liye extremely useful hai.
14. Common JEE Traps ⚠️
❌ Trap 1: Electric field ko scalar treat karna.
✅ Correct: Electric field is a vector quantity.
❌ Trap 2: Multiple fields ko magnitude ke basis par directly add kar dena.
✅ Correct: Pehle direction determine karo, then vectorially add karo.
❌ Trap 3: Negative charge ka field charge se away assume karna.
✅ Correct: Positive charge → away; Negative charge → towards.
❌ Trap 4: Charge double hone par distance effect ko ignore karna.
✅ Correct: E ∝ Q/r²
❌ Trap 5: Infinite sheet ka electric field distance ke saath decrease karna.
✅ Correct: Ideal infinite sheet ke liye E = σ/(2ε₀), independent of distance.
❌ Trap 6: Conductor ke inside electric field non-zero assume karna.
✅ Correct: Electrostatic equilibrium mein E = 0.
❌ Trap 7: Electric force aur electric field ko same quantity samajhna.
✅ Correct: F = qE; field charge-independent source property hai at a point, while force placed charge par depend karta hai.
15. JEE Main Problem-Solving Strategy
Electric field ke questions solve karte waqt ek fixed approach follow karo:
STEP 1 → Source Charge Identify Karo
Point charge hai, line charge hai, sheet hai ya conductor?
STEP 2 → Correct Formula Select Karo
Point charge ke liye kQ/r², line charge ke liye λ/(2πε₀r), sheet ke liye σ/(2ε₀).
STEP 3 → Direction Determine Karo
Positive charge se field away aur negative charge ki taraf field towards.
STEP 4 → Superposition Apply Karo
Multiple charges hain to individual fields ko vectorially combine karo.
STEP 5 → Symmetry Check Karo
Midpoint, centre ya symmetric arrangement ho to cancellation immediately identify karo.
STEP 6 → Units Check Karo
Distance ko metres aur charge ko coulombs mein convert karna mat bhoolna.
16. Quick Revision ⚡
Electric Field
E = F/q₀
Vector quantity.
SI Unit → N/C
Point Charge
E = kQ/r²
+Q → Away
−Q → Towards
Electric Force
F = qE
Superposition
Enet = ΣE
Infinite Line
E = λ/(2πε₀r)
Infinite Sheet
E = σ/(2ε₀)
Conductor
Inside → E = 0
Just Outside → E = σ/ε₀
Charge Densities
λ = Q/L
σ = Q/A
ρ = Q/V
17. Final Revision Box 🔥
Electric Field
E = F/q₀
Point Charge
E = kQ/r²
Electric Force
F = qE
Superposition
Enet = ΣE
Infinite Line Charge
E = λ/(2πε₀r)
Infinite Sheet
E = σ/(2ε₀)
Conductor
Inside → E = 0
Just Outside → E = σ/ε₀
Direction
+Q → Away
−Q → Towards
Most Important
E is a vector quantity.
Golden Rule
MAGNITUDE → DIRECTION → VECTOR ADDITION → ANSWER
```18. Practice Questions for JEE Main
Q1. A point charge produces an electric field E at distance r. What will be the field at distance 2r?
Q2. If the charge producing an electric field is doubled while distance remains constant, how does E change?
Q3. Two equal positive charges are placed symmetrically. What is the net electric field at their midpoint?
Q4. Two equal and opposite charges are separated by a distance. What is the direction of electric field at the midpoint?
Q5. Write the electric field due to an infinite line charge having linear charge density λ.
Q6. Write the electric field due to an infinite plane sheet of surface charge density σ.
Q7. What is the electric field inside a conductor in electrostatic equilibrium?
Q8. A charge q is placed in an electric field E. Find the force acting on it.
19. PDF – Complete Study Notes
Students can use the embedded PDF below for quick offline revision of the Electric Field topic.
20. Frequently Asked Questions – FAQs
Q1. What is electric field?
Electric field is the force experienced by a unit positive test charge. Its formula is E = F/q₀.
Q2. Is electric field a scalar or vector quantity?
Electric field is a vector quantity, because it has both magnitude and direction.
Q3. What is the SI unit of electric field?
The SI unit is N/C (Newton per Coulomb).
Q4. What is the electric field due to a point charge?
For a point charge Q at distance r:
E = kQ/r²
Q5. What is the direction of electric field due to a positive charge?
For a positive charge, electric field is directed away from the charge.
Q6. What is the direction of electric field due to a negative charge?
For a negative charge, electric field is directed towards the charge.
Q7. What is the superposition principle?
When multiple charges are present, the net electric field is the vector sum of the individual electric fields.
Q8. What is the electric field inside an electrostatic conductor?
In electrostatic equilibrium, the electric field inside the conductor is zero.
Q9. Does the electric field due to an infinite sheet depend on distance?
No. For an ideal infinite plane sheet, E = σ/(2ε₀), so the field is independent of distance.
Q10. What is the difference between electric field and electric force?
Electric field is the force per unit positive test charge, while force on a charge q placed in the field is given by F = qE.
21. Final Thoughts
Electric Field ko strong banane ka best way hai formula ke saath direction aur vector nature ko equally important samajhna.
JEE Main ke liye sabse important formulas hain:
E = F/q₀
E = kQ/r²
F = qE
Enet = ΣE
E = λ/(2πε₀r)
E = σ/(2ε₀)
Aapko saath hi yaad rakhna chahiye:
+Q → Field Away
−Q → Field Towards
Conductor Inside → E = 0
Har numerical mein pehle magnitude calculate karo, phir direction identify karo aur multiple charges hone par vector superposition apply karo.
Ek simple JEE rule yaad rakho:
MAGNITUDE → DIRECTION → VECTOR ADDITION → ANSWER
Ye approach Electric Field ke basic se JEE Main-level questions tak aapko systematically solve karne mein help karegi.