Electric Flux Closed Surface

Description:

A surface which is closed from all the sides is called a closed surface and if you light a bulb inside , no light should come out of it.

We have two type of closed surfaces −

• A closed sphere
• A cube or a cuboid

In this topic we will be experimenting using a cube which is closed and  also has 6 plane surfaces. All the surfaces are having a particular area and each area is having a particular direction.

In a closed surface the direction of A→ is always be pointing normally outward the surface.

Each surface is given names (1,2,3,4,5,6) as shown in figure.

Let, the cuboid be placed in an electric field, then the total flux linked with it will be calculated by adding the flux linked with each surface of the cuboid.

We know that Φ = EACos θ

• If we take the Area (1), then the flux linked with it will be −

  Φ_E1 = EAcos(180) = -EA

  Since, the area vector is outside the area (1) and E→ in opposite direction of the A→. So the angle between (E→ and A→ is 180^o)

• If we take the surface (2) where the angle between (E→ and A→ is 90^o)

  Then the flux linked with it will be −

  Φ_E2 = EA Cos(90) = 0

• Similarly for surface (3) the angle between (E→ and A→ is 0^o)

  Then the flux linked with it will be −

  Φ_E3 = EAcos(0) = EA

• For surface (4) the angle between (E→ and A→ is 90^o)

  Then the flux linked with it will be −

  Φ_E4 = EAcos(90) = 0

• For surface (5) the angle between (E→ and A→ is 90^o)

  Then the flux linked with it will be −

  Φ_E5 = EAcos(90) = 0

• For surface (6) the angle between (E→ and A→ is 90^o)

  Then the flux linked with it will be −

  Φ_E6 = EAcos(90) = 0

So, the total electric flux due to all the area will be given by the closed integral of all the electric flux linked with each surface.

Φ_E = ∮ dΦ = 0

So, Flux linked with a closed surface in an electric field is Φ_E = ∮E→ . dA→ But in case of a closed cuboid flux linked is zero.

Note − Flux for two or more surfaces cannot be calculated together at a time. As angle formed by different surface with respect to the electric field will be different therefore, for each surface electric flux will change.