Ampere's Law

[Sriman Dutta]

Hello everybody,

The Ampere's Law states that the total [math]B[/math]-field generated by a conducting element of length [math]l[/math] is directly proportional to the current element [math]I[/math].

Thus,

[math] Bl = \mu_0 I[/math]

Where [math]\mu_0[/math] is the constant of proportionality.

But, will the constant of proportionality be [math]\mu_0[/math] or [math] \mu_0 \mu_r [/math] ?

These two sites use two different formulations.....

http://www.electrical4u.com/biot-savart-law/

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html#c1

Edited December 23, 2016 by Sriman Dutta

[studiot]

Both are right!

 

The Biot-Savart page is simply more complete in that it takes into account the medium via [math]{\mu _r}[/math]

For air and many purposes such as the space between sub atomic particles [math]{\mu _r}[/math] is so close to 1 that we often ignore it.

That is what is done in your second link from hyperphysics.

A more satisfactory way to deal with this is to use

[math]\mu = {\mu _0}{\mu _r}[/math]

Then there is no ambiguity.

Incidentally your hyperphysics link has some good pictures of the circular magnetic field lines around straight conductors carrying current.

Look carefully at these and think about your other thread on crossed wires.

[Sriman Dutta]

So, it's better to use [math]\mu_0 \mu_r [/math] for accuracy. Thanks...