00:01
Hi there, so for this problem, we are told to derivate an expression for the capacitance of a part of plate capacitor with a conducting slab inserted between its plates.
00:11
Assume that the slab thickness to be less than the plate separation.
00:15
So we're going to call the thickness as t, the thickness of the slab, and the separation between the plates as the distance t.
00:25
Now with that said, we are also led that q, e capital q, is the charge on the plates of the capacitors.
00:40
And when a conducting slough of thickness t is inserted between the plates, then the original electric field that we're going to call e -0, so this is the original electric field.
01:04
It sits over a distance that is the separation is the difference between d minus the thickness d.
01:12
And inside the metallic plate electric field is zero.
01:16
So net potential difference between the place is that net potential difference is the electric field times the distance of separation, which is d minus t.
01:29
So we know that the electric field inside this is epsilon d charge density this times the separation d minus the thickness and this divided by epsilon sub 0 which is a constant.
01:49
In here we know that the charge density surface the charge surface density is the charge capital q divided by the area now, we know that the capacitance is equal to the charge divided by the potential difference.
02:09
So we just need to simply substitute the expression from before...