- #1

## Main Question or Discussion Point

hi guys,i wanted to know if any of u have a method for calculatind the electricfield of a uniformly electrified closed loop of radius 'r' over all the space?

:grumpy:

:grumpy:

- Thread starter psuchetic_edition
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- #1

hi guys,i wanted to know if any of u have a method for calculatind the electricfield of a uniformly electrified closed loop of radius 'r' over all the space?

:grumpy:

:grumpy:

- #2

MalleusScientiarum

You're going to have to be more specific. I'm not 100% clear on what the problem is.

- #3

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I think it would require spherical integration and some trig (i.e. it's probably going to be long and messy).

First, I would draw a picture. Mine has the ring on the x-y plane centered at the origin.

Next, I would pick a random point on the graph. I drew one off to the side in the upper half of the space. I would then draw a vector from the origin to the point. I call this position vector

To find the electric field, you need to first find the potential at that point. To do this, you need to find the contribution from the entire ring. This means you need to integrate along the ring.

The potential due to one small infintesimal portion of the ring is a function of the length of

I can't really go into much detail without actually solving it. Perhaps there's an easier way that someone knows.

- #4

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this is the best option:psuchetic_edition said:hi guys,i wanted to know if any of u have a method for calculatind the electricfield of a uniformly electrified closed loop of radius 'r' over all the space?

:grumpy:

One can use Coulombs law to calculate the E field, use polar coordinates because you will have to integrate over the closed circular wire.

or

You can use Ampere's law to calculate the magnetic field and from the Maxwell equations, calculate the E field...There are several options

marlon

Last edited:

- #5

Meir Achuz

Science Advisor

Homework Helper

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On the axis of the ring, that is a standard elementary textbook problem.

It is easier to first find the potential, and then the E field will be the gradient of the potential.

To find the potential off the axis, you first expand it in a power series.

Then the power series can be related to a Legendre polynomial expansion in cos\theta to find the potential off the axis. (I assume this is what you meant by "over all space".) This off-axis problem is done in some advanced texts.