Electric field between two plates

hiya


Why is electric field ( EF ) between two oppositely charged parallel plates uniform ( homogenous ), meaning in all points electric force on test charge will be the same ?

Suppose the plates are 10 cm apart. Net electric force on test charge in the middle of the two plates ( 5 cm away from each plate ) would be

Code:

electric force caused by plate one ... E1 
electric force caused by plate two ... E2
net electric force                 ... E
E                                  ... E1 + E2

e_plate1 ... charge of plate 1
e_plate2 ... charge of plate 2
e_plate1 = - e_plate2 = 2

e ... test charge = 1


r[1] ... distance of test charge from plate 1
r[2] ... distance of test charge from plate 2

k ... electrostatic constant


E1 = k * e_plate1 * e / (r[1]^2) = k * 2 * 1 / 5^2 
E2 = k * e_plate2 * e / (r[2]^2) = k * 2 * 1 / 5^2

E = E1 + E2 = k * (4/25)

If we then move test charge 1 cm towards first plate (test charge's distance is now 4 cm from first plate and 6 cm from left plate),then net electric force would be

Code:

E1 = k* e_plate1 * e / (r[1]^2) = k * 2 * 1 / 4^2 
E2 = k* e_plate2 * e / (r[2]^2) = k * 2 * 1 / 6^2

E = E1 + E2 = k * (2/16 + 2/36) 


k * (4/25) = / = k * (2/16 + 2/36) 

2)

Is EF between two parallel plates uniform only when the amount of charge on both plates is the same ( plate 1 has charge -A and plate two has charge A)? If so, why?


3)

Formula for electric field between two plates that are infinitely large is E = D / e[0]. How did we derive it?

Code:

e[0] ... permittivity of free space
D    ... Electric-Flux Density

4)

Even though formula is the same, how did we derive E = D/[e[0]] for EF ( I know electric forces are different at edges of plates, but within the central region between the plates magnitude of EF should be same for both infinitely and finitely large plates ) between two finitely large plates?

thank you

 

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This formula only applies for point charges, and even then there should only be one charge in the formula, not two.

The magnitude of the field near a flat plate is E = ρ/2ε₀, where ρ is the charge density (charge per unit area) of the plate, and a positive E is a field directed away from the plate.

 

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You didn't read my entire post. I wrote that E stands for electric force not electric field.
On the other hand, I should use different letter for electric force.

 

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Textbooks I've seen typically use E or φ (phi) for the field and F for the force.

 

My physics text book uses calculus to derive the field formulas that start with a point charge (that decreases in strength at 1/r^2) then to a infinitely long charged cylinder (that decreases in strength at 1/r) and then to a infinite charged plane (that does not decrease in strength = in fact "r" is not in the equation)

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You can see that the field near an infinitely large flat plate is constant by applying Gauss' law in it's integral form. There's no need to do any calculus.

 

It doesn't seem logical that infinite charged plane would have constant strentgh.Afterall the reason this plane is charged is cos of point charges it contains, and electric fields of point charges decrease by distance.

 

Ok. Imagine a flat, infinitely large horizontal charged plate, and a charge Q some height h above this plate. All the charges in the plate pull on the charge, but they don't all pull in the same direction. Some, right under the charge, pull it almost straight down, and others, much further away, pull it nearly horizontally. Since the horizontal components of the force all cancel out, it's only the vertical component you need to worry about.

Now let's consider a charge P on the plate very far away from Q, where the force it exerts on Q is nearly horizontal. The vertical component of the force will be negligible. If Q moves up (h increases), the sine of the angle increases a lot faster than the distance² between P and Q, so the vertical component of the force will increase with h (at least to begin with). If you like, as Q moves away from the plate, you can consider that the area of the plate that exerts most (eg. 90%) of the force on Q increases.

Dunno if that helped. It's not a proof, but it should make the constant-field-near-a-flat-plate idea seem more plausible.

 

Yes, it did help, but I'm even more confused now than before. In my other thread it was said that charge can only pull on one test charge at the time. So suppose that 4 test charges appear in the electric field created by charges residing on object's surface.

I will call charge A one of the many charges residing on object's surface. Now this charge may at the same time help to pull on all 4 test charges ( this goes for all object's charges ). But if you read my other thread it's been said it can only pull one one charge at the time.

 

No. Every charge pushes/pulls every other charge all the time.