- #1

Leo Liu

- 353

- 156

- Homework Statement
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- Relevant Equations
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I saw the following equation on page 31 in Purcell's EM textbook.

$$F=\epsilon_0\int_{E_1}^{E_2} E\, dE=\frac 2 {\epsilon_0} (E_2^2-E_1^2)$$

Here, F is the force on a unit area.

And then he claims that since ##E_2-E_1=\sigma/\epsilon_0##, the equation can be further simplified to

$$F=\frac 1 {\epsilon_0}(E_1+E_2)\sigma$$

However, I think the correct coefficient in the last part of first equation should be the inverse of what it is now (##\frac{\epsilon_0}{2}## instead), as only then can I obtain the second expression. I have no idea why the author wrote the equation this way. To give it a little bit of background, dE is the change in the electric field of a thin layer of a charged sphere, E1 is the the electric field inside, and E2 is the electric field outside. Could someone explain?

$$F=\epsilon_0\int_{E_1}^{E_2} E\, dE=\frac 2 {\epsilon_0} (E_2^2-E_1^2)$$

Here, F is the force on a unit area.

And then he claims that since ##E_2-E_1=\sigma/\epsilon_0##, the equation can be further simplified to

$$F=\frac 1 {\epsilon_0}(E_1+E_2)\sigma$$

However, I think the correct coefficient in the last part of first equation should be the inverse of what it is now (##\frac{\epsilon_0}{2}## instead), as only then can I obtain the second expression. I have no idea why the author wrote the equation this way. To give it a little bit of background, dE is the change in the electric field of a thin layer of a charged sphere, E1 is the the electric field inside, and E2 is the electric field outside. Could someone explain?

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