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Science Forum Index » Physics - Electromagnetic Forum » EM problem
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| Pmb |
Posted: Sun Dec 17, 2006 11:35 pm |
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Guest
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Hi folks
I need someone to double check my work. In Ohanian's EM book he has
the following question under the problem section
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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 |
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| Casey Hawthorne |
Posted: Mon Dec 18, 2006 10:00 pm |
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Guest
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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 |
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| Pmb |
Posted: Wed Dec 20, 2006 9:39 am |
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Guest
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"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 |
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| Casey Hawthorne |
Posted: Wed Dec 20, 2006 10:14 pm |
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Guest
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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 |
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| Pmb |
Posted: Wed Dec 20, 2006 10:54 pm |
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Guest
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"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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