A sphere of radius r has total charge q the volume charge...

A sphere of radius R has total charge Q. The volume charge density (C/m3) within the sphere is ?(r)=C/r2, where C is a constant to be determined. 1. Use Gauss's law to find an expression for the magnitude of the electric field strength E a) inside the sphere, r<R b) outside the sphere r>=R in terms of Q and R. Express your answer in terms of variables r, R, Q and epsilon naught 2. sketch a plot for the Electric field versus distance

Transcript

00:01 Hello students.

00:03 In this problem, we have a solid sphere of radius capital r and charge capital q.

00:13 Charge is capital q and its radius is capital r and this charge is known uniformly distributed over it.

00:20 And the charge density is given c by r square, coulom per meter cube.

00:29 It is volume charge density, that is charge per end volume.

00:33 Okay first of all we have to calculate the value of c to this to find this value of see what we are doing we are taking a spherical shell of radius r and with d r its thickness is taken as d r its small thickness is taken as d r it means the volume of this shell will be 4 pi r squared here this d r is very minute it is charge on this shell will be charge density c by r square of course we can write it row dv charge of density at r distance into volume of this shell and the volume of this shell is surface area into thickness we are writing this value now dq equals to c by r square c by r square 4 pi r square d r what it is it is a volume of this shell 4 pi r square d r clearly r c r square is canceling out we will cancel this r square of course.

01:39 It means the dq is equal to this dq is equals to c4 pi dr.

01:49 If we calculate total charge in this shell by doing integration, integrating this side from 0 to capital r.

02:00 Integrating this side from 0 to capital r, it will give us total charge capital q, 0 to q.

02:09 Clearly intuition of dr is r after putting limit it will be capital r q equal to c time 4 pi r we were looking for the value of c it means c is equals to it means clearly c is equals to q upon 4 pi r it is our first part of the question calculation of c and we got it the value of c clearly unit will be coulampar it is coulomb per meter.

02:47 Okay.

02:49 It is the value of c.

02:50 Now what we have to do, we have to find the electric field inside this solid sphere and outside this sphere...

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