Electric Flux Class 12

 Electric Flux

    The total number of electric field lines passing normally through an area is called electric flux related to that area.

Electric flux is represented by `\phi`.

Electric Flux

Electric flux is directly proportional to the electric field so `\phi \prop E`.

Electric flux is directly proportional to the area vector so `\phi \prop A`.

Electric flux is directly proportional to `cos\theta` so `\phi \prop cos\theta`.

So we can say

`\phi \prop E A cos\theta`

`\phi = E A cos\theta`

`\phi = \vec E.\vecA`

Hence, Electric flux `\phi` is a scalar product of electric field `\vec E` and area vector `\vec A`.

If the area is very small then 

`d\phi = \vec E.d\vecA`

Total flux

`\int d\phi = \int \vec E.d\vecA`

`\phi = \int \vec E.d\vecA`

Special case

(1)     If `\theta = 0^\circ` then `cos0^\circ = 1`,

`\phi = \int E dA cos\theta`

`\phi = \int E dA cos 0`

`\phi = \int E dA cos 0`

`\phi = \int E dA`

`\phi = E \int dA`

`\phi = E A`        `(\because \int dA = A)`

(2)    If `\theta = 90^\circ` then `cos90^\circ = 0`,

`\phi = \int E dA cos\theta`

`\phi = \int E dA cos 90`

`\phi = \int E dA cos 90`

`\phi = \int E dA (0)`

`\phi = 0`

`\star`    The S.I. unit of electric flux is `\frac{Nm^2}{C}` or V m.

`\star`    The dimensional of electric flux is `[M^1L^3T^{-3}A^{-1}]`

`\star`    Electric flux is a scalar quantity.

`\star`    Electric flux is a scalar quantity and has an SI unit of `{\text{newton} \times \text{meters}^2}/\text{Coulomb}`.

Electrostatics Class 12 Chapter 1 Detailed Notes

Numerical Questions on Electric Flux

Q.    Determine the electric flux through an electric field `\vec E = (200\hat i + 300\hat j) V m^{-1}` placed in area `\vec A 5 \times 10^{-3}\hat j m^2` (Answer 1.5 V m)

Q.    A cylinder is placed in a uniform electric field `\vec E` whose direction is along the axis of electric field. Show that the total electric flux through the cylinder is zero.

Q.    A circular sheer of radius 5 cm placed in the uniform electric field of `5 \times 10^5 V m^{-1}` such that its plane makes an angle `30^\circ` with the field. Determine the electric flux through the sheet. (Answer 1.96`\times 10^3 V m`)

MCQs on Electric Flux with Answer

Q    What is the value of total flux through the faces of the cube with the sides of length a if a charge Q is placed at corner A of the cube is -

(1)    `frac{q}{\epsilon_0}`

(2)    `frac{q}{2\epsilon_0}`

(3)    `frac{q}{4\epsilon_0}`

(4)    `frac{q}{8\epsilon_0}`

Answer    (4)    `frac{q}{8\epsilon_0}`

Q    What is the value of electric flux (`\phi`) on a plane of area `1 m^2` on which an electric field of 2 V/m crosses with an angle of ` 30` ^\circ` .

(1)    1 Vm

(2)    2 Vm

(3)    3 Vm

(4)    4 Vm

Answer    (1)    1 Vm

Q    Determine the electric flux of a flat square having an area of `10 m^2` is a uniform electric field of 8000 N/C passing perpendicular to it

(1)    `8 \times 10^5 {Nm^2}/C`

(2)    `8 \times 10^4 {Nm^2}/C`

(3)    `16 \times 10^5 {Nm^2}/C`

(4)    `4 \times 10^4 {Nm^2}/C`

Answer    (2)    `8 \times 10^4 {Nm^2}/C`

Q    The electric flux through a cubical Gaussian surface enclosing net charge q is `q/\epsilon_0`. While the electric flux through one face of a cube is -

(1)    `\phi = \frac{q}{\epsilon_0}`

(2)    `\phi = \frac{q}{6\epsilon_0}`

(3)    `\phi = \frac{q}{4\pi\epsilon_0}`

(4)    `\phi = \frac{q}{4\epsilon_0}`

Answer    (2)    `\phi = \frac{q}{6\epsilon_0}`

Q    A point charge q is placed at a distance `a/2` directly above the center of the square of side a. The electric flux through the square is -

(1)    `\phi = \frac{q}{\epsilon_0}`

(2)    `\phi = \frac{q}{6\epsilon_0}`

(3)    `\phi = \frac{q}{4\pi\epsilon_0}`

(4)    `\phi = \frac{q}{4\epsilon_0}`

Answer    (2)    `\phi = \frac{q}{6\epsilon_0}`  

Short Answer type Question

Q.    What is flux in electrical?

 Answer:   The total number of electric field lines passing normally through an area is called electric flux related to that area.

More Questions

1. What is electric flux?

2. How is electric flux represented?

3. What are the factors that electric flux is directly proportional to?

4. What is the equation that relates electric flux, electric field, and area vector?

5. What happens to the electric flux when the area is very small?

6. What is the formula for the total flux?

7. What happens to the electric flux when the angle between the electric field and the area vector is 0 degrees?

8. What happens to the electric flux when the angle between the electric field and the area vector is 90 degrees?

9. What are the SI unit and dimensions of electric flux?

10. Is electric flux a scalar or vector quantity?

Answers

1. Electric flux is a measure of the electric field passing through a given surface. It represents the total number of electric field lines passing through a surface per unit area.

2. Electric flux is represented by the symbol Φ (phi).

3. Electric flux is directly proportional to the strength of the electric field, the surface area of the surface through which the field passes, and the cosine of the angle between the electric field and the surface normal.

4. The equation that relates electric flux (Φ), electric field (E), and area vector (A) is given by Φ = E ⋅ A, where ⋅ represents the dot product.

5. When the area is very small, the electric flux becomes smaller as well, since there is less surface area for the electric field lines to pass through.

6. The formula for the total flux depends on the specific situation and the geometry of the surface. For example, for a closed surface, the total flux is given by the surface integral of the electric field over the entire surface.

7. When the angle between the electric field and the area vector is 0 degrees, the electric flux is maximized. In this case, all the electric field lines pass perpendicularly through the surface, resulting in maximum flux.

8. When the angle between the electric field and the area vector is 90 degrees, the electric flux becomes zero. In this case, the electric field lines are parallel to the surface, and none of them pass through it.

9. The SI unit of electric flux is the volt-meter (V·m), and its dimensions are` [M^1 L^3 T^-3 I^-1]`, where M represents mass, L represents length, T represents time, and I represents electric current.

10. Electric flux is a scalar quantity. Although it has a direction associated with the surface normal, it does not possess the properties of a vector since it does not obey the rules of vector addition.

Electric Flux Questions

11. A charge of `10^-6` C is placed at the center of a cube of side 1 m. What is the electric flux through each face of the cube?

(Answer: `2.57 \times 10^-5 N m^2 C^-1`)

12. A point charge of `10^-6` C is placed in a uniform electric field of `10^4 N C^-1`. What is the electric flux through a spherical surface of radius 1 m, if the surface is (a) concentric with the charge, (b) perpendicular to the field lines, and (c) parallel to the field lines?

(Answers: (a) `10^-5 N m^2 C^-1`, (b) `10^-5 N m^2 C^-1`, (c) 0)

13. A dipole is placed in a uniform electric field. What is the angle between the dipole moment and the electric field if the torque on the dipole is maximum?

(Answer: 90 degrees)

14. A dipole is placed in a uniform electric field. What is the potential energy of the dipole if the angle between the dipole moment and the electric field is 0 degrees?

(Answer: 0)

15. A dipole is placed in a uniform electric field. What is the potential energy of the dipole if the angle between the dipole moment and the electric field is 180 degrees?

(Answer: maximum)