Gauss's law problem

1. Oct 16, 2004

purplex76

An infinitely long solid cylinder radius R1 lies with it's central cylindrical axis lying along the x axis. it is made of a non-conducting material. It has a volume charge density that varies with readius as follows... p(r)=A.r (C/m^3)
where A is a constant. Consider a cylindrical Gaussian surface of length L, radius r, concentric with the x axis.

1) Derive a formula for the amount of charge enclosed by this Gaussian surface for r is greater than or equal to R1, and for r is less than or equal to R1

2) Use gauss's Law to find an expression for the electric field as a function of r in these two regions

3) graph the magnitude of the electric filed for these two regions.

i would appreciate any help with this question because it is really stumping me.....Thanks!

2. Oct 16, 2004

Tide

What exactly have you tried so far and what is your thinking?

3. Oct 17, 2004

Theelectricchild

Oh wait one more thing, please post this type of question under "college level help" thank you.

4. Oct 17, 2004

ukamle

Solution to the Gauss law problem:

Volume charge density= Ar
For r > a

Let the radius of cylindrical Gaussian surface be r

E . 2. pi. r. l = integral {( 2*pi.A.l.r. dr / e0 ), 0 , a}

[integral { (), ,} denotes-- () - integral funciton then the limits]

e0 -> permittivity of free space

[ E = A. (a^2)/ (2*r) ] ............... Solution

For r<=a

E . 2*pi.r.l = integral { (2*pi.A.l.r dr/ e0), 0, r}

[ E=A.r/2 ] .............. Solution

5. Oct 19, 2004

purplex76

that doesn't make sense to me. Isn't the problem more complex than 2 integrals, because i got no credit for the integrals i put down, being somewhat similar to the ones you replied with.

6. Oct 24, 2004

ukamle

gauss law problem

$$\mbox{i m sorry i forgot to divide by } \epsilon_0\mbox{. Divide the solutions by} \epsilon_0 \mbox{. I feel, that is the correct solution.}$$

7. Oct 24, 2004

ukamle

another method

You may also use the differential form of Gauss law for cylindrically radial field. It goes something like this:
$$\frac{d(E.r)}{dr} = \frac{\rho r}{\epsilon_0}$$

Make $$\rho$$ as a function or r and integrate over proper limits.