# Field of an infinite plate

#### manenbu

1. Homework Statement

From Resnick and Halliday:

A metal plate 8 cm on a side carries a total charge of 60 microC. Using the infinite plate approximation, calculate the electric field 0.5 mm above the surface of the plate near the plate's center.

2. Homework Equations

(1) $$E = \frac{\sigma}{\epsilon_0}$$
or
(2) $$E = \frac{\sigma}{2\epsilon_0}$$
$\sigma$ being charge density.
3. The Attempt at a Solution

I got a bit confused here. Equation (1) should be used when the plate is a conductor, and equation (2) should be used when the plate is an insulator, according to the explanation in the book.
However, when I use equation (1) to calculate, I get 106MN/C, and in the answers in the back of the book it says it should be 53 MN/C. Either I used the wrong equation, or I should have used half of the charge.
What went wrong?

And honestly, I really did not understand why there are 2 different equations for each situation (conductor, insulator). I tried deriving them on my own but no success in gaining real understanding, so I'd be really glad if someone could shed some light on the subject.

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#### collinsmark

Homework Helper
Gold Member
A metal plate 8 cm on a side carries a total charge of 60 microC. Using the infinite plate approximation, calculate the electric field 0.5 mm above the surface of the plate near the plate's center.
I calculate an answer that differs by a factor of 10 from the given answer. Are you sure that the problem statement specifies 60 μC instead of say, 6.0 μC?
2. Homework Equations

(1) $$E = \frac{\sigma}{\epsilon_0}$$
or
(2) $$E = \frac{\sigma}{2\epsilon_0}$$
$\sigma$ being charge density.
3. The Attempt at a Solution

I got a bit confused here. Equation (1) should be used when the plate is a conductor, and equation (2) should be used when the plate is an insulator, according to the explanation in the book.
However, when I use equation (1) to calculate, I get 106MN/C, and in the answers in the back of the book it says it should be 53 MN/C. Either I used the wrong equation, or I should have used half of the charge.
What went wrong?

And honestly, I really did not understand why there are 2 different equations for each situation (conductor, insulator). I tried deriving them on my own but no success in gaining real understanding, so I'd be really glad if someone could shed some light on the subject.
I'm not familiar with Resnick and Halliday text. However, I doubt a textbook would make such a mistake.

Equation (1) applies to the situation where you have two separate, oppositely charged plates, and you're looking for the electric field in between them. This is the situation when working with a parallel plate capacitor (without a dielectric).

Equation (2) applies to a single charged plate.

The difference in application between the equations has nothing really to do with the plate(s) being conducting or insulating. Rather its a matter of whether you have one or two plates.

Capacitors will invariably be constructed of conducting plates (otherwise it wouldn't function as a capacitor). Maybe that's from where the confusion stems.

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