Problem 5.3 The space between two concentric conducting...

Problem 5.3 The space between two concentric conducting spherical shells (radii 1.70 cm and 1.20 cm) is filled with a substance ($k$ = 23.5). A potential difference of 73.0 V is applied across the inner and outer shells. Determine (a) the capacitance of the device, (b) the total charge on the inner shell, and (c) the charge polarized on the dielectric. Answer: 0.107 nF, 7.78 nC, 7.75 nC

Transcript

00:01 This question we've been given that there are two concentric conducting spherical shells and the radius are, so b value has been given to us as 1 .7 into 10 ratio to the power minus 2 meters.

00:15 The radius a is given to us as 1 .2 into 10 raised to the power minus 2 meters.

00:21 And they've also given that in between the plates, in the space between the spherical plates, there's a dielectric which has constant 6 .91 and the potential drop across the plates of this capacitor is given to us as 73 volts.

00:38 So the first thing that we have to find out in this question in part a is the capacitance of this device.

00:44 So since it's based out of spherical plates so we'll write down the capacitance as 4 pi epsilon knot k and in bracket we'll write ab upon b minus a.

01:00 So this is a general formula.

01:02 Now let's put in all the values.

01:04 So 4 pi epsilon not we can write it down.

01:10 So this can be further written as let's write down k first which is 6 .91 upon.

01:16 So i make it 1 by 4 pi epsilon not which is 9 into 10 ratios of 9 and into in the bracket we'll write a into b.

01:25 So a into b is 1 .6 .6.

01:26 7 into 10 raised to the power minus 2 into 1 .2 into 10 raised to the power minus 2 and below we'll take the difference between them so 1 .7 minus 1 .2 into 10 raised to the power minus 2.

01:42 So this value finally the value of capacitance of this device comes out to be 31 .4 pico ferrets.

01:50 So this is the answer to our first part.

01:53 Now let's move on to the second part of the question.

01:56 Here we are asked to find out what is the free charge q on the inner shell.

02:01 So free charge can obviously be calculated directly using formulas.

02:06 So it's q is equal to cv.

02:08 So c is the capacitance of the device that we found out over here.

02:12 So it's 31 .4 into 10 raised to the power minus 12.

02:17 And into the voltage is given to us as 73...

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