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Author Topic: How to verify Biot-Savart Law?  (Read 90966 times)
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Fu-Kwun Hwang
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on: January 29, 2004, 09:29:48 pm » posted from:,,Satellite Provider

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The magnetic field set up at point P by the current element i ds
    turn out to be
    The above equation is called the Biot-Savart law.


The vector dB is perpendicular both to ds (which is the direction of the current)
    and to the unit vector r directed from the element to the point P.

The magnetic of dB is inversely proportional to r2 , where r is the distance from the element to the point P.

However, the current must form a loop. You will not have only a small current element.
All the current elements along the current loop can contribute to the magnetic field at point P.
How do we measure magnetic field dB just due to a small current element?
Here is an ideal!



There is no magnetic field in the direction of the current element.
The above two green lines meet at blue dot P.
Current elements from green lines will not produce magnetic field at point P.
The magnetic field at point P is due to current elements from two yellow line sections.
We can keep one of the current element much further away from point P.

Now we have a way to measure the magnetic field just due to one current element.
    Click near the right yellow line section and drag the mouse up/down to change its length.
    Click near the left yellow line section and drag the mouse up/down or left/right
      to change its length and location.

    The point P moves when you make the above changes.
    The magnetic field at point P is shown at the top left corner.
    Click at the DC current source to change its polarity.
    You can enter value for the current source into the text Field.
    The moving black points represent the electrons moving with average drift velocity.
    If you enter a larger value for the current , the electrons will move faster.

    Keep increasing the value for the current, until you see the electrons
      changing directions -> moving faster -> changing direction ...!

    Why is that ? Is there something wrong with the program?
    Look at tires of a car when it is accelerating!
    Those tires seem to be rotated faster and then change direction ...!


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Reply #1 on: January 30, 2004, 11:11:24 am » posted from:,,Satellite Provider

Subject: Thanks for great BioSavart
Date: Mon, 24 Aug 1998 22:16:57 -0700
From: "Sunpainter" <sunpaint@gte.net>
To: <hwang@phy03.phy.ntnu.edu.tw>
I was looking for something on the shape of circuit for very small circuit
trying to predict some electromagnetic field changes in the circuit.
I will be using very, very small current.
Your simulation was incredibly, wonderfully helpful!
If I had to do all the math for each current change, it would have taken me forever.
Now I have my figures. THANK YOU THANK YOU!
It is for a strange little generator I am building.
Thank you!
K. Hodge Southern California
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Reply #2 on: May 28, 2004, 08:35:12 am »

nipple
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Worldtraveler
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Reply #3 on: May 14, 2008, 02:42:27 pm »

Thank You.
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Reply #4 on: January 25, 2009, 12:19:54 am » posted from:Baltimore,Maryland,United States

This is fascinating.  Will you please explain why the current changes direction?  It does not seem to make sense to me.
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Fu-Kwun Hwang
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Reply #5 on: January 25, 2009, 09:26:50 am »

You can click the DC source to change it's polarity.
I think your question is not why it change direction but why flow direction is opposite to the electric field.
Because the moving black points represent the electrons moving with average drift velocity.
It represent electron flow (not the current flow). It was written a few lines below the applet.
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