⚡ Electric Field Lines: Properties, Representation & Field Due to Point/System of Charges
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1. What are Electric Field Lines?
Electric field lines are imaginary lines used to represent the electric field around a charged body.
The tangent to a field line at any point gives the direction of the electric field at that point.
E = F/q₀
where:
- E = electric field
- F = force experienced by test charge
- q₀ = positive test charge
2. Electric Field Due to a Point Charge
For a point charge Q, the electric field at distance r is:
E = k|Q|/r²
where:
k = 1/(4πε₀)
For a positive charge, field lines point outward.
For a negative charge, field lines point inward.
🔴 Positive charge → Field lines emerge outward.
🔵 Negative charge → Field lines terminate inward.
⚡ Greater line density → Stronger electric field.
🔵 Negative charge → Field lines terminate inward.
⚡ Greater line density → Stronger electric field.
3. ⚡ Practical Animated Electric Field Simulator
Change Charge & Observe Field Lines
Q = +5 μC
r = 4 m
Scale = 5
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Field lines show the direction of E. Change Q to see attraction/repulsion pattern.
Live Calculation:
Electric field magnitude: 0 N/C
Direction: Away from charge
Electric field magnitude: 0 N/C
Direction: Away from charge
4. Important Properties of Electric Field Lines
1. Direction
The tangent at any point gives the direction of electric field.
The tangent at any point gives the direction of electric field.
2. Density
Closer field lines represent a stronger electric field.
Closer field lines represent a stronger electric field.
3. Never Intersect
Two electric field lines cannot intersect because the electric field has only one direction at a point.
Two electric field lines cannot intersect because the electric field has only one direction at a point.
4. Positive Charge
Lines originate from positive charges.
Lines originate from positive charges.
5. Negative Charge
Lines terminate on negative charges.
Lines terminate on negative charges.
6. Conductors
Field lines are perpendicular to the surface of a conductor in electrostatic equilibrium.
Field lines are perpendicular to the surface of a conductor in electrostatic equilibrium.
5. Representation of Field Lines
| Charge/System | Field Line Pattern | Direction |
|---|---|---|
| +Q | Radially outward | Away from charge |
| −Q | Radially inward | Towards charge |
| +Q and −Q | Curved lines | + → − |
| Two + charges | Lines bend away from central region | Outward |
| Two − charges | Lines terminate on both charges | Inward |
6. Electric Field Due to a System of Charges
When several charges are present, the net electric field is the vector sum of the electric fields produced by each charge individually.
E⃗net = E⃗₁ + E⃗₂ + E⃗₃ + ...
For n charges:
E⃗net = ΣE⃗ᵢ
This is called the principle of superposition.
🔥 JEE Method:
1️⃣ Consider each source charge separately.
2️⃣ Calculate its electric field.
3️⃣ Draw the correct direction.
4️⃣ Resolve vectors if required.
5️⃣ Add all electric-field vectors.
1️⃣ Consider each source charge separately.
2️⃣ Calculate its electric field.
3️⃣ Draw the correct direction.
4️⃣ Resolve vectors if required.
5️⃣ Add all electric-field vectors.
7. Practical Example – Two Charges
Suppose two positive charges are placed on a straight line and a point P lies between them.
At P:
- Field due to the left charge points towards the right.
- Field due to the right charge points towards the left.
Enet = E₁ − E₂
If E₁ = 10 N/C and E₂ = 6 N/C:
Enet = 10 − 6 = 4 N/C
Net Electric Field = 4 N/C towards the right
8. Electric Field at the Midpoint of Equal Like Charges
For two equal positive charges +Q and +Q placed symmetrically:
At the midpoint, the two electric fields have equal magnitude but opposite directions.
Therefore:
E₁ = E₂
and:
Enet = 0
At midpoint: E = 0
9. Electric Field Lines of an Electric Dipole
An electric dipole consists of two equal and opposite charges separated by a small distance.
Field lines originate from the positive charge and terminate on the negative charge.
Electric Dipole = +q and −q
The field lines are curved and symmetric about the dipole axis.
10. ⭐ JEE Quick Revision Rules
Positive charge → Lines OUT
Negative charge → Lines IN
Field-line density ∝ Electric-field strength
Field lines never intersect
E⃗net = ΣE⃗ᵢ
E ∝ 1/r²
Negative charge → Lines IN
Field-line density ∝ Electric-field strength
Field lines never intersect
E⃗net = ΣE⃗ᵢ
E ∝ 1/r²
11. 📝 30 MCQs with Solutions
1. Electric field lines originate from:
A. Negative charge
B. Positive charge
C. Neutral charge
D. Both equally
Answer: B. Positive charge
2. Electric field lines terminate on:
A. Positive charge
B. Negative charge
C. Neutral charge only
D. None
Answer: B. Negative charge
3. The tangent to an electric field line gives:
A. Magnitude of charge
B. Direction of electric field
C. Electric potential only
D. Resistance
Answer: B. Direction of electric field
4. Electric field lines can:
A. Intersect each other
B. Never intersect
C. Always form circles
D. Stop randomly
Answer: B. Never intersect
5. Closely spaced electric field lines indicate:
A. Weak field
B. Strong field
C. Zero field
D. Zero charge
Answer: B. Strong field
6. The electric field due to a point charge varies as:
A. r
B. r²
C. 1/r
D. 1/r²
Answer: D. 1/r²
7. The SI unit of electric field is:
A. N/C
B. C/N
C. J/C
D. C/m
Answer: A. N/C
8. Electric field is a:
A. Scalar
B. Vector
C. Constant
D. Dimensionless quantity
Answer: B. Vector
9. Field lines around a positive point charge are:
A. Radially inward
B. Radially outward
C. Circular
D. Parallel only
Answer: B. Radially outward
10. Field lines around a negative point charge are:
A. Outward
B. Inward
C. Circular
D. Random
Answer: B. Inward
11. Net electric field due to several charges is found by:
A. Scalar addition only
B. Vector addition
C. Multiplication
D. Division
Answer: B. Vector addition
12. The superposition principle states:
A. E = E₁E₂
B. E⃗ = ΣE⃗ᵢ
C. E = E₁/E₂
D. E = 0 always
Answer: B. E⃗ = ΣE⃗ᵢ
13. Electric field lines represent:
A. Electric field direction and relative strength
B. Charge mass
C. Resistance
D. Current
Answer: A
14. At electrostatic equilibrium, field lines at a conductor surface are:
A. Parallel to surface
B. Perpendicular to surface
C. Circular
D. Random
Answer: B. Perpendicular to surface
15. Two equal positive charges are placed symmetrically. Electric field at midpoint is:
A. Maximum
B. Zero
C. Infinite
D. Negative
Answer: B. Zero
16. Electric field lines are:
A. Real physical wires
B. Imaginary representation
C. Electric currents
D. Charges
Answer: B. Imaginary representation
17. The number of field lines is proportional to:
A. Magnitude of charge
B. Mass
C. Resistance
D. Temperature
Answer: A. Magnitude of charge
18. Field lines of an electric dipole originate from:
A. −q and end at +q
B. +q and end at −q
C. Both start at −q
D. Neither
Answer: B. +q and end at −q
19. Electric field at a point is force per unit:
A. Mass
B. Positive test charge
C. Distance
D. Energy
Answer: B
20. If distance from a point charge doubles, electric field becomes:
A. 2E
B. E/2
C. E/4
D. 4E
Answer: C. E/4
21. If charge Q is doubled, electric field at same distance becomes:
A. E/2
B. 2E
C. 4E
D. E
Answer: B. 2E
22. Electric field lines are denser where:
A. Electric field is stronger
B. Electric field is weaker
C. Charge is zero
D. Potential is zero
Answer: A
23. The electric field inside an ideal conductor in electrostatic equilibrium is:
A. Maximum
B. Zero
C. Infinite
D. Variable
Answer: B. Zero
24. Two field lines intersecting at a point would imply:
A. Two electric-field directions at one point
B. Zero charge
C. Maximum potential
D. Zero force
Answer: A
25. For a negative charge, electric field direction is:
A. Away from charge
B. Towards charge
C. Perpendicular always
D. Circular
Answer: B. Towards charge
26. For a positive charge, electric field direction is:
A. Towards charge
B. Away from charge
C. Zero
D. Circular
Answer: B. Away from charge
27. The electric field is strongest where field lines are:
A. Far apart
B. Closely packed
C. Absent
D. Parallel only
Answer: B. Closely packed
28. The electric field due to a point charge depends on:
A. Q and r
B. Only mass
C. Only time
D. Resistance
Answer: A. Q and r
29. Which principle is used for a system of charges?
A. Superposition principle
B. Archimedes principle
C. Bernoulli principle
D. Pascal law
Answer: A. Superposition principle
30. The correct expression for the field of a point charge is:
A. E = kQr²
B. E = kQ/r²
C. E = kr²/Q
D. E = Qr²/k
Answer: B. E = kQ/r²
12. ⭐ Final Revision
Electric Field: E = F/q₀
Point Charge: E = k|Q|/r²
Positive Charge: Field lines → OUT
Negative Charge: Field lines → IN
Field-line density: Indicates field strength
Multiple Charges: E⃗net = ΣE⃗ᵢ
Field lines never intersect.
Point Charge: E = k|Q|/r²
Positive Charge: Field lines → OUT
Negative Charge: Field lines → IN
Field-line density: Indicates field strength
Multiple Charges: E⃗net = ΣE⃗ᵢ
Field lines never intersect.
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