How Does the Electric Field Vary with Distance in a Cylindrical Shell?

[JayKo]

Homework Statement

Consider an infinitely long cylindrical metallic shell with a line of charge within and
coincides with the axis of the cylindrical shell as shown in Figure . How does E field vary
with r?

Homework Equations

E.A=q/$$\epsilon$$

E=E field, A = surface area

The Attempt at a Solution

The Electric field within the inner circle of cylinder +Q pointing toward outer space.assuming charge at the wire is +Q. however the the area inside the thickness of the pipes has ZERO Electric field because the inner surface of the pipe is induced with -Q, while the outer surface is having total charge of +Q.

Area surrounding the pipe surface having E field pointing outward.

http://img441.imageshack.us/img441/2706/wiredinapipevi8.th.jpg
is this explanation make sense, or how should i write in a more presentable manner? thanks

 

[Doc Al]

What you say is correct (except that you use Q instead of the charge per unit length), but you didn't do what was asked: Express the field as a function of r.

Hint: Call the charge per unit length $\lambda$. Use Gauss's law to find an expression for E(r) in each of those three regions.

 

[arunbg]

Well your explanation is quite correct, but you would also want to give the exact expression for the electric field at varying distances from the line of charge. Just use Gauss' law.

Edit: I am gettin old for this lol

 

[JayKo]

What you say is correct (except that you use Q instead of the charge per unit length), but you didn't do what was asked: Express the field as a function of r.

Hint: Call the charge per unit length $\lambda$. Use Gauss's law to find an expression for E(r) in each of those three regions.

hi Dr. Al. ok, here is the derivation of the E(r) and r relationship.

$$\Phi$$=E A = Q / $$\epsilon$$.

therefore, E = $$\frac{\lambda}{2\pi\epsilon*r}$$.

[just couldn't get the latex working]
The E field is = lamba / (2*pi*r*epsilon) ]


From this, we predicted the E field is inversely proportional to the distance from the wire to the pipe, r. however the only exception is when E field is inside the wall of the pipe. it is ZERO as mention above.

 

[JayKo]

Well your explanation is quite correct, but you would also want to give the exact expression for the electric field at varying distances from the line of charge. Just use Gauss' law.

Edit: I am gettin old for this lol

LOL, my explanation is at post #4. thanks for the reply.

 

[Doc Al]

Looks good to me! (I'd mention that you used a cylindrical Gaussian surface. If its length is L, the charge within that surface is $\lambda$ L.)

 

[JayKo]

Looks good to me! (I'd mention that you used a cylindrical Gaussian surface. If its length is L, the charge within that surface is $\lambda$ L.)

yeah, q= $\lambda$* length
while derive it, length was cancel out with the cylinder length.

btw, my final doubt is, since we are ask to consider a INFINATELY long cylindrical shape, we still consider it as length, L. which only this that my explanation can establish.

 

[Doc Al]

Cosidering an infinitely long cylinder allows you to assume that the field is uniform and radial (by symmetry) in your Gaussian section, regardless of where along the axis you place it. If the pipe or line charge were finite, and you were near the end, you'd expect some non-radial components (edge effects).

 

[JayKo]

Cosidering an infinitely long cylinder allows you to assume that the field is uniform and radial (by symmetry) in your Gaussian section, regardless of where along the axis you place it. If the pipe or line charge were finite, and you were near the end, you'd expect some non-radial components (edge effects).

Hi Doc, i finally got the whole big picture of this. just a minor clarification, [regardless of where along the axis you place it.] are you referring to the position of the charged wires is not necessary at the centre of the pipe? because i feel this is not real intituitive, as the formula suggest, the E field do depend on the radius.correct me if i m wrong and misinterpret the meaning.


{If the pipe or line charge were finite, and you were near the end, you'd expect some non-radial components (edge effects)} this part i can understand. thanks again.

 

[JayKo]

hi Doc, i finally got your meaning of your post #08. please marked this thread as solved!.thanks .

 

[Doc Al]

Excellent. (Looks like I forgot to respond to your last post. Oops! But you have it now.)

As far as marking the thread solved, you should be able to do it: Click on thread tools and you should see an option.