Cant understand some step in a solution

1. Aug 29, 2009

nabliat

here is the problem and solution:
http://i26.tinypic.com/2vvm8vm.jpg
http://i31.tinypic.com/nqwq4n.jpg

i solved the 1st subquestion.
my problem starts with the second subquestion:
i understood how they got this expression
$$E=\frac{\epsilon_0}{\epsilon}E_0$$

but i dont know what they do next
what law principle are they doing in the next 3 lines??

why the integral equals the expression that they show??

Last edited: Aug 29, 2009
2. Aug 29, 2009

nabliat

replied in a wrong place

3. Aug 29, 2009

kuruman

The principle is that the electric field can be derived from the electric potential

$$\vec{E} = -\vec{\nabla U}$$

from which it follows that

$$V =-\int\vec{E} \cdot \vec{d \ell}$$

The line integral is taken along a straight line from one plate to the other and needs to be split into two terms because the E-field changes when the dielectric-vacuum boundary is crossed. That's why you get two terms with two different E values.

Does this make sense?

4. Aug 29, 2009

nabliat

$$\vec{E} = -\vec{\nabla U}$$
this means that the field is the divergent of the potential

$$V =-\int\vec{E} \cdot \vec{d \ell}$$
why are we starting to look for the potenitial
we are asked to find the total field
??

in the result i was not presented with the total electric field
but with sepated fields that i knew them already before the integral part

??

Last edited: Aug 29, 2009
5. Aug 29, 2009

kuruman

My explanation was how they got equations (7) - (9). They did the line integral in two steps because there are two different electric fields between the plates. After doing the integral, they solve the equation to find E0 in terms of the voltage, which we assume is a given quantity. Once you have E0, you can find E.

6. Aug 29, 2009

ok thanks :)