Question

In the notes for capacitance and dielectrics, section 5.2 I calculated the electric field within a coaxial capacitor by considering the enclosed charge +Q to be resolvable into (surface density).(Area enclosed by the Gaussian surface). I got E= (surface density).a/(r.e0), where r is the arbitrary but fixed radius of the Gaussian cylinder. But the notes is saying I should instead use the line density such that E=lambda/(2.Pi.e0.r). But the strangest thing is that I got exactly the same result as in the notes although I began with something different. How is that conceivable?

Answer 1

In physics u have many ways and its not must u to follow what u have seen so that means u have to make research to compare what u have learnt dude

Answer 2

Well, just want to check against someone else's opinion. Thought about peer assisted review, you know. :-)

Answer 3

Line density and cylindrical surface density have the same geometrical properties (cylindrical symmetry).

Within your Gaussian surface, the charge will be the same and your field will decrease with 1/r all the same.

Now, your capacitance will have a different expression if your inner plate is an actual cylinder of radius R1.

You must find a capacitance with \(\ln \Large \frac{R_2}{R_1}\) in the denominator.