Why is electric flux Nm²/C and not area per field strength?

[Miike012]

Units for electric flux is Nm²/C = (electric Field Strength)(Surface Area).

However the units of electric flux are confusing because I though the definition of Electric flux was

The number of electric field lines through an area of surface. Therefore I though Electric flux would have had units of (Surface Area)/(Electric Field Strength).

Please look in paint doc for my reasoning.
1.Black square is a plane of area da
2.Red square = Portion of plane that one E-Field Vector covers = da/n = (Integer value) where n>1

Side Note: Reason why I made da/n = Integer was because I wanted to make sure that a fraction of an E-Vect was not passing through da which would mean that the other fraction of the same E-Vect would remain outside da ( or Not passing through da) (Not sure if that matters though).

**3.Each Field vector passing through da has equal magnitude.

4. Rest of explanation is in paint doc.

Clearly my understanding is off. Can someone please help me understand. Thank you.

 

[Doc Al]

However the units of electric flux are confusing because I though the definition of Electric flux was

The number of electric field lines through an area of surface. Therefore I though Electric flux would have had units of (Surface Area)/(Electric Field Strength).

The electric field strength (the field) can be thought of as the number of field lines per unit area. So, flux (number of field lines) = (Electric Field Strength) x (Surface Area).

Please look in paint doc for my reasoning.
1.Black square is a plane of area da
2.Red square = Portion of plane that one E-Field Vector covers = da/n = (Integer value) where n>1
**3.Each Field vector passing through da has equal magnitude.

The field is uniform, thus the number of field lines per unit area is uniform. The total flux would be E*da.

 

[Miike012]

The field is uniform, thus the number of field lines per unit area is uniform. The total flux would be E*da.

I know that I just created an example to explain to you why I thought the units of E-flux should be (Mag of E-Field entering surface)/(surface Area).
I wasn't interested in the equation only the units.

 

[Miike012]

The electric field strength (the field) can be thought of as the number of field lines per unit area

I would have never known that by the electric field equation which has units of N/c = Vm... No where in the units do you see units for area...

 

[Miike012]

I suppose intuitively that I could think of the E-field as number of field lines per area as you explained it because the stronger the E-Field the more condensed the field lines would be therefore taking up less area at a certain distance from the source of the E-Field compared to a weaker E-field at the same distance from the source producing the weaker field.

 

[Doc Al]

I suppose intuitively that I could think of the E-field as number of field lines per area as you explained it because the stronger the E-Field the more condensed the field lines would be therefore taking up less area at a certain distance from the source of the E-Field compared to a weaker E-field at the same distance from the source producing the weaker field.

Exactly.

Realize that field lines are just a way to help visualize things. They don't really exist! What exists is the field, which has a value everywhere.

 

[Doc Al]

I would have never known that by the electric field equation which has units of N/c = Vm... No where in the units do you see units for area...

As I said in my last post, 'field lines' are just tools for visualization. Thus you won't see 'lines' or area in any standard units for field.

The standard unit for flux isn't 'number of lines' but E*Area = Nm²/C.