Azeotropes

ELECTRIC FLUX

INTRODUCTION

Electric flux is a fundamental concept in Electrostatics that helps us understand how electric fields interact with surfaces. It represents the number of electric field lines passing through a given surface and provides a way to quantify the strength of an electric field over an area. The concept becomes especially powerful when studied with Gauss's Law, which states that the total electric flux through a closed surface depends only on the charge enclosed within that surface. This principle simplifies the analysis of electric fields in symmetric situations such as spheres, cylinders, and planes. Electric flux is not only important for theoretical physics but also has practical applications in areas like capacitors, electric field mapping, and understanding charge distribution.

1. Definition of Electric Flux

Electric flux is defined as the total number of electric field lines passing through a given surface.

In simple terms,

it measures how much electric field “flows” through a surface.

2. Formula of Electric Flux

Φ = E A cosθ

Where:
Φ = Electric flux
E = Electric field
A = Area
θ = Angle between field and area vector

3. Unit of Electric Flux

SI Unit = Nm²/C (Newton meter² per Coulomb)

4. Dimensions of Electric Flux

Electric flux = E × A
Dimensions of E = [M L T⁻³ A⁻¹]
Dimensions of A = [L²]

Dimensions of Flux = [M L³ T⁻³ A⁻¹]

5. Gauss’s Theorem (Gauss’s Law)

According to Gauss's Law:

The total electric flux through any closed surface is equal to 1/ε₀ times the total charge enclosed.

Φ = Q/ε₀
Where:
Q = Enclosed charge
ε₀ = Permittivity of free space

6. Applications of Gauss’s Law

1. Calculation of Electric Field

Used to find electric field for:

• Spherical charge distribution
• Infinite line charge
• Infinite plane sheet

A.Electric Field for spherical charge distribution

B.Electric Field for spherical infinite line charge

C.Electric Field for infinite plane sheet of charge

2. Understanding Charge Distribution

• Charges in a conductor stay on the surface
• Electric field inside a conductor is zero

3. Symmetry-Based Problems

Simplifies calculations when system has:

• Spherical symmetry
• Cylindrical symmetry
• Planar symmetry

4. Flux Calculations

Helps find flux without knowing detailed field distribution.

5. Used in Devices

Applied in:

• Capacitors
• Electrostatic shielding
• Electric field mapping

Quick Summary (for exams)

• Flux = EA cosθ
• Unit = Nm²/C
• Depends on E, A, θ
• For closed surface: depends only on enclosed charge

CONCLUSION

In conclusion, electric flux provides a simple yet powerful way to analyze electric fields and their interaction with surfaces. It highlights that the total flux through a closed surface is independent of the shape or size of the surface and depends solely on the enclosed charge, as explained by Gauss's Law.

Understanding electric flux helps build a strong foundation for solving complex problems in electrostatics and plays a key role in advanced topics of physics. Its applications in real-life systems further demonstrate its importance, making it an essential concept for students studying Class 12 physics.

MCQ

Here are 49 MCQs on Electric Flux (Class 12 Physics) based on Electrostatics:

Basic Concepts (1–15)

1.Electric flux is a measure of:

A. Charge
B. Electric field strength
C. Number of electric field lines passing through a surface
D. Potential

2. SI unit of electric flux:

A. N/C
B. Nm²/C
C. C/N
D. Volt

3. Electric flux depends on:

A. Electric field only
B. Area only
C. Orientation of surface
D. All of these

4. Flux is maximum when angle between field and area vector is:

A. 0°
B. 30°
C. 60°
D. 90°

5. Flux is zero when angle is:

A. 0°
B. 45°
C. 90°
D. 180°

6. Electric flux is a:

A. Scalar
B. Vector
C. Tensor
D. None

7. Formula of electric flux:

A. E × A
B. E + A
C. EA cosθ
D. EA sinθ

8. Flux through closed surface is given by:

A. Ohm’s law
B. Faraday’s law
C. Gauss’s law
D. Coulomb’s law

9. Unit of electric field:

A. N/C
B. Nm²/C
C. Volt
D. Joule

10. Electric flux is:

A. Always positive
B. Always negative
C. Can be positive or negative
D. Always zero

11. Area vector is:

A. Along surface
B. Perpendicular to surface
C. Parallel to field
D. Zero

12. Flux depends on:

A. Shape of surface
B. Orientation
C. Field strength
D. All

13. Closed surface is also called:

A. Loop
B. Gaussian surface
C. Circuit
D. Path

14. Flux inside conductor:

A. Maximum
B. Minimum
C. Zero
D. Infinite

15. Flux is proportional to:

A. E/A
B. EA
C. E²A
D. A/E

Gauss’s Law & Applications (16–35)

16. Gauss’s law relates flux with:

A. Area
B. Charge enclosed
C. Field
D. Distance

17. Mathematical form of Gauss’s law: Φ = Q/ε₀
ε₀ is called:

A. Permeability
B. Permittivity of free space
C. Conductivity
D. Resistivity

18. Value of ε₀:

A. 8.85 × 10⁻¹² F/m
B. 9 × 10⁹
C. 1.6 × 10⁻¹⁹
D. 3 × 10⁸

19. If no charge is enclosed:

A. Flux = 1
B. Flux = ∞
C. Flux = 0
D. Flux = E

20. Flux through sphere depends on:

A. Radius
B. Charge inside
C. Area
D. Shape

21. Flux through cube enclosing charge:

A. Depends on size
B. Depends on shape
C. Depends only on charge
D. Zero

22. If charge is outside surface:

A. Flux ≠ 0
B. Flux = 0
C. Flux = infinite
D. Depends

23. Unit of ε₀:

A. F/m
B. N/C
C. Volt
D. Ohm

24. Electric field lines:

A. Start from negative charge
B. End on positive
C. Start from positive
D. Circular

25. More field lines mean:

A. Weak field
B. Strong field
C. Zero field
D. Constant field

26. Flux is negative when:

A. Field enters surface
B. Field leaves surface
C. No field
D. Charge zero

27. Flux is positive when:

A. Field enters
B. Field leaves
C. Field zero
D. Charge zero

28. Electric flux through closed surface:

A. Depends on shape
B. Depends on area
C. Depends only on enclosed charge
D. Depends on field direction

29. Gauss’s law is valid for:

A. Only symmetric shapes
B. All closed surfaces
C. Only spheres
D. Only cubes

30. Field inside hollow conductor:

A. Zero
B. Infinite
C. Maximum
D. Variable

31. Charge resides on:

A. Inside conductor
B. Surface
C. Both
D. None

32. Flux density is:

A. E
B. EA
C. E/A
D. A/E

33. Electric flux is:

A. Vector
B. Scalar
C. Complex
D. Tensor

34. Flux through open surface:

A. Defined
B. Not defined
C. Infinite
D. Zero

Numerical/Conceptual (35–49)

35. Flux = EA cosθ, θ = 0 → Flux:

A. 0
B. EA
C. E/A
D. EA²

36. θ = 90°, flux:

A. EA
B. 0
C. E
D. A

37. If E doubles, flux:

A. Same
B. Doubles
C. Halves
D. Zero

38. If area doubles:

A. Flux same
B. Flux doubles
C. Flux halves
D. Zero

39. Flux independent of:

A. Charge inside
B. Shape
C. Field
D. Area

40. Flux through closed surface with +q:

A. Positive
B. Negative
C. Zero
D. Infinite

41. Flux through closed surface with −q:

A. Positive
B. Negative
C. Zero
D. Infinite

42. If charge is at center:

A. Unequal flux
B. Equal distribution
C. Zero
D. Infinite

43. Total flux divided among surfaces:

A. Unequal
B. Equal
C. Depends
D. Zero

44. Electric flux is analogous to:

A. Current flow
B. Heat
C. Pressure
D. Work

45. Gauss’s law derived from:

A. Coulomb’s law
B. Newton’s law
C. Ohm’s law
D. Kirchhoff’s law

46. Closed surface flux:

A. Depends on area
B. Depends on enclosed charge
C. Depends on field
D. Depends on shape

47. Flux lines crossing outward:

A. Positive
B. Negative
C. Zero
D. Infinite

48. Flux lines inward:

A. Positive
B. Negative
C. Zero
D. Infinite

49. Electric flux is maximum when:

A. θ = 0°
B. θ = 90°
C. θ = 180°
D. θ = 45°

CASE STUDY

Case Study: Electric Flux Around a Charged Sphere

A small metallic sphere is placed in a vacuum and given a positive charge +Q. Around this sphere, different imaginary closed surfaces (Gaussian surfaces) are drawn—some are spherical, some cubical, and some irregular in shape. The electric field lines originate from the positively charged sphere and spread outward uniformly in all directions.

According to Gauss's Law, the total electric flux through any closed surface depends only on the charge enclosed inside the surface, not on its shape or size. The electric flux through a closed surface is given by:

Φ = Q/ε₀

Where:

Φ = Electric flux

Q = Charge enclosed

ε₀ = Permittivity of free space

Situation-Based Questions

Q1.

If the Gaussian surface is a sphere enclosing the charge +Q, what is the electric flux?

A. Zero

B. Qε₀

C. Q/ε₀

D. Depends on radius

Q2.

If the surface is changed from a sphere to a cube (still enclosing +Q), the flux will:

A. Increase

B. Decrease

C. Remain same

D. Become zero

Q3.

If the charge is moved outside the Gaussian surface, flux becomes:

A. Maximum

B. Zero

C. Infinite

D. Negative

Q4.

If the enclosed charge is doubled (2Q), flux becomes:

A. Same

B. Doubled

C. Halved

D. Zero

Q5.

What happens to flux if the surface size increases?

A. Increases

B. Decreases

C. Remains same

D. Becomes zero

Q6.

Electric field lines for a positive charge:

A. Enter the charge

B. Leave the charge

C. Circular

D. Random

Q7.

If half the charge is inside and half outside the surface, flux is:

A. Q/ε₀

B. Q/2ε₀

C. Zero

D. Infinite

Q8.

Flux is negative when:

A. Field lines leave surface

B. Field lines enter surface

C. No charge

D. Field is zero

Key points

• Electric flux measures field lines crossing a surface.
• It is a scalar quantity.
• Depends only on enclosed charge, not shape/size.

ASSERTION- REASON

Here are Assertion–Reason questions on Electric Flux from Electrostatics (Class 12 level):

Directions:

Choose the correct option:

A. Both Assertion and Reason are true, and Reason is the correct explanation

B. Both are true, but Reason is not the correct explanation

C. Assertion is true, Reason is false

D. Assertion is false, Reason is true

Questions

1.

Assertion (A): Electric flux through a closed surface depends only on the enclosed charge.

Reason (R): Electric flux is independent of the shape and size of the surface.

2.

Assertion (A): Electric flux is zero if no charge is enclosed.

Reason (R): Equal number of field lines enter and leave the surface.

3.

Assertion (A): Electric flux is a scalar quantity.

Reason (R): It is the dot product of electric field and area vector.

4.

Assertion (A): Electric flux can be negative.

Reason (R): Flux is negative when field lines enter the surface.

5.

Assertion (A): Electric flux through a surface increases with increase in area.

Reason (R): Flux = EA cosθ.

6.

Assertion (A): Flux is maximum when surface is perpendicular to field.

Reason (R): cos 0° = 1.

7.

Assertion (A): Flux is zero when surface is parallel to field.

Reason (R): cos 90° = 0.

8.

Assertion (A): Electric flux through a closed surface does not depend on external charges.

Reason (R): External charges produce equal inward and outward flux.

9.

Assertion (A): Electric field inside a conductor is zero.

Reason (R): Charges reside on the surface of conductor.

10.

Assertion (A): Electric flux through a sphere enclosing a charge depends on its radius.

Reason (R): Larger radius means larger area.

11.

Assertion (A): Flux through an open surface is well defined.

Reason (R): It depends on orientation of the surface.

12.

Assertion (A): Electric flux is proportional to electric field.

Reason (R): Flux = EA cosθ.

13.

Assertion (A): Electric flux through a closed surface is always positive.

Reason (R): Flux depends on sign of charge enclosed.

14.

Assertion (A): Electric field lines never intersect.

Reason (R): At a point, electric field has unique direction.

15.

Assertion (A): Electric flux is zero for a charge placed outside the surface.

Reason (R): No net field lines pass through the surface.

Tip for Exams

Most Assertion–Reason questions in this chapter are based on:

• Gauss's Law
• Sign of flux (inward vs outward)
• Dependence on enclosed charge

WORKSHEET

Here’s a practice worksheet on Electric Flux (Class 12) from Electrostatics. (Try solving first — answers are given at the end.)

Electric Flux Worksheet

Section A: Basic Numericals

1.An electric field of 4 × 10³ N/C passes normally through a surface of 3 m². Find electric flux.

2. A surface of area 2 m² is placed in a field of 10 N/C at 60°. Find flux.

3. Electric field = 15 N/C, area = 5 m², angle = 90°. Find flux.

4.Flux through a surface is 40 Nm²/C, area is 4 m². Find electric field (θ = 0°).

5. A field of 8 N/C passes through area 6 m² at 0°. Find flux.

Section B: Gauss’s Law Based (Use Gauss's Law)

6. A charge of 8.85 × 10⁻¹² C is enclosed. Find flux.

7. Find flux if enclosed charge is 2 × 10⁻⁸ C.

8. Flux through a closed surface is 200 Nm²/C. Find enclosed charge.

9. If no charge is enclosed, what is flux?

10. A charge of –4 × 10⁻⁹ C is enclosed. Find flux.

Section C: Concept-Based

11. What is flux when θ = 0°? (in terms of E and A)

12. What is flux when θ = 90°?

13. If electric field doubles, what happens to flux?

14. If area is halved, what happens to flux?

15.Flux is zero when angle is ______.

Section D: Mixed Numericals

16. Electric field = 12 N/C, area = 3 m², angle = 60°. Find flux.

17. Flux = 60 Nm²/C, area = 6 m², angle = 0°. Find electric field.

18. A charge of 1.77 × 10⁻¹¹ C is enclosed. Find flux.

19. Field = 20 N/C, area = 2 m², angle = 30°. Find flux.

20. Flux = 0, area ≠ 0, field ≠ 0. Find angle.

Answer Key

1. 1.2 × 10⁴ Nm²/C
2. 10 Nm²/C
3. 0
4. 10 N/C
5. 48 Nm²/C
6. 1 Nm²/C
7. ≈ 2260 Nm²/C
8. 1.77 × 10⁻⁹ C
9. 0
10. ≈ –452 Nm²/C
11. EA
12. 0
13. Doubles
14. Halves
15. 90°
16. 18 Nm²/C
17. 10 N/C
18. 2 Nm²/C
19. ≈ 34.6 Nm²/C
20. 90°