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Pmb
Posted: Sun Dec 17, 2006 11:35 pm
Guest
Hi folks

I need someone to double check my work. In Ohanian's EM book he has
the following question under the problem section
----------------------------------------------
A circular annulus of inner radius R1 and outer radius R2 has a
uniform charge density sigma. What is the electric field on the axis of the
annulus at a distance z from the center?
----------------------------------------------
I worked this out and got

E = pi*sigma*z { 1/sqrt( z^2 + R2^2) - 1/sqrt( z^2 + R1^2) }

Ohanian has twice this value in his answer section. Which answer do
you get after you work this out? Thanks.

Best wishes

Pete
Casey Hawthorne
Posted: Mon Dec 18, 2006 10:00 pm
Guest
For the electric field of a uniformly charged thin ring along the axis
I get the following:

E = (1/(4 * pi * epsilon-naught))((q*z)/((R^2 + z^2)^(3/2)))

where R is the radius of the ring and the ring has charge q


Starting from:

dEz = (1/(4 * pi * epsilon-naught))(q/(2*pi))(z/((R^2 +
z^2)^(3/2)))dTheta



"Pmb" <peter102560_nospam@comcast.net> wrote:

Quote:
Hi folks

I need someone to double check my work. In Ohanian's EM book he has
the following question under the problem section
----------------------------------------------
A circular annulus of inner radius R1 and outer radius R2 has a
uniform charge density sigma. What is the electric field on the axis of the
annulus at a distance z from the center?
----------------------------------------------
I worked this out and got

E = pi*sigma*z { 1/sqrt( z^2 + R2^2) - 1/sqrt( z^2 + R1^2) }

Ohanian has twice this value in his answer section. Which answer do
you get after you work this out? Thanks.

Best wishes

Pete

--

Regards,
Casey
Pmb
Posted: Wed Dec 20, 2006 9:39 am
Guest
"Casey Hawthorne" <caseyhHAMMER_TIME@istar.ca> wrote in message
news:hbheo29mfm05hnesfre8q298v38v7a5bgm@4ax.com...
Quote:
For the electric field of a uniformly charged thin ring along the axis
I get the following:

E = (1/(4 * pi * epsilon-naught))((q*z)/((R^2 + z^2)^(3/2)))

where R is the radius of the ring and the ring has charge q

You made an error somewhere. The answer should be a function of both the
inner diameter and thd outter diameter of the *annulus* (a flat disc with
smaller disk punched out of the center, e,g, a washer that would go around a
bolt).

Thanks

Pete

Quote:


Starting from:

dEz = (1/(4 * pi * epsilon-naught))(q/(2*pi))(z/((R^2 +
z^2)^(3/2)))dTheta



"Pmb" <peter102560_nospam@comcast.net> wrote:

Hi folks

I need someone to double check my work. In Ohanian's EM book he has
the following question under the problem section
----------------------------------------------
A circular annulus of inner radius R1 and outer radius R2 has a
uniform charge density sigma. What is the electric field on the axis of
the
annulus at a distance z from the center?
----------------------------------------------
I worked this out and got

E = pi*sigma*z { 1/sqrt( z^2 + R2^2) - 1/sqrt( z^2 + R1^2) }

Ohanian has twice this value in his answer section. Which answer do
you get after you work this out? Thanks.

Best wishes

Pete

--
Regards,
Casey
Casey Hawthorne
Posted: Wed Dec 20, 2006 10:14 pm
Guest
I was doing the electric field of a uniformly charged thin ring!

I thought you could generalize it to an annulus/washer with both an
inner and an outer diameter.

I wasn't sure whether you were doing a homework question or not!



"Pmb" <peter102560_nospam@comcast.net> wrote:

Quote:

"Casey Hawthorne" <caseyhHAMMER_TIME@istar.ca> wrote in message
news:hbheo29mfm05hnesfre8q298v38v7a5bgm@4ax.com...
For the electric field of a uniformly charged thin ring along the axis
I get the following:

E = (1/(4 * pi * epsilon-naught))((q*z)/((R^2 + z^2)^(3/2)))

where R is the radius of the ring and the ring has charge q

You made an error somewhere. The answer should be a function of both the
inner diameter and thd outter diameter of the *annulus* (a flat disc with
smaller disk punched out of the center, e,g, a washer that would go around a
bolt).

Thanks

Pete



Starting from:

dEz = (1/(4 * pi * epsilon-naught))(q/(2*pi))(z/((R^2 +
z^2)^(3/2)))dTheta



"Pmb" <peter102560_nospam@comcast.net> wrote:

Hi folks

I need someone to double check my work. In Ohanian's EM book he has
the following question under the problem section
----------------------------------------------
A circular annulus of inner radius R1 and outer radius R2 has a
uniform charge density sigma. What is the electric field on the axis of
the
annulus at a distance z from the center?
----------------------------------------------
I worked this out and got

E = pi*sigma*z { 1/sqrt( z^2 + R2^2) - 1/sqrt( z^2 + R1^2) }

Ohanian has twice this value in his answer section. Which answer do
you get after you work this out? Thanks.

Best wishes

Pete

--
Regards,
Casey

--

Regards,
Casey
Pmb
Posted: Wed Dec 20, 2006 10:54 pm
Guest
"Casey Hawthorne" <caseyhHAMMER_TIME@istar.ca> wrote in message
news:f7rjo2p0ajp7o5n2lt9kutiod656nbnjgs@4ax.com...
Quote:
I was doing the electric field of a uniformly charged thin ring!

I thought you could generalize it to an annulus/washer with both an
inner and an outer diameter.

I wasn't sure whether you were doing a homework question or not!

Yes. I am. Its been years since I've brushed up on my EM so I like to keep
sharp by doing problems every once in a while. Its not for school. Its just
for me and the author whom I send corrections to when I find them. Since he
sent me an autographed copy for free this is the least I could do... but I
always do it anyway. :D

Pete
 
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