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30 Jul 2009 23:14:14 IST

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Ampere circuital law and biot savart law

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If we take current carrying straight wire of length, say l, and we want to find magnetic field at point p.

Using Ampere circuital law along circle(perpendicular to wire and centre lying on the wire), the circulation of magnetic field is µ_oi

Further, Magnetic field is tangential to this circle every where and also equal.

Hence implication by the law is

B(2πr)= µ_oi

B= µ_oi\(2πr)

where r à radius of circle

however if use biot savart law here then we find that

B= {µ_oi(cosφ₁-cosφ₂)}\ 4πr

Where φ₁and φ₂ à angle between line joining point p and ends of wire

I am not able to understand what mistake I have committed in applying ampere circuital law here

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Comments (8)

Kshitiz Kumar

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Joined: 29 Apr 2009

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31 Jul 2009 20:52:49 IST

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frnd you hav made no mistake in deriving both the formula in biot-savart 's law put

as the circle would subtend angle from 0 to 180 degrees on the long wire

Deepak Aggarwal

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2 Aug 2009 00:26:18 IST

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Simple substitute now values of cos.

Saurabh kumar pal

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2 Aug 2009 09:36:26 IST

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I think my question is creating some confusion. perhaps you all are thinking that circle is taken along the perpendicular bisector of the wire, may be. But i must make you clear that center of the circle taken, can be anywhere on the length of wire. and see wire is not infinitly long. In this situation(what i have explicated in question). application of ampere circuital law is not applicable. Although it generates same answer as biot savart law for field at perpendicular bisector.

Usha Sree

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7 Aug 2009 16:37:42 IST

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After using biot savart law, we will get the mag field as mui(cos@d@)/4pir this should be integrated from -@1 to @2

and so the mag field would be mui(sin@1+sin@2)/4pir

and i think ampere circuital law cannot be applied for the finite wire.

Correct me if i m wrong

Anand Narayanan

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12 Aug 2011 19:51:21 IST

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Y ampers law not applicable for finite wire ??

rishabh

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12 Aug 2011 20:00:34 IST

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amperes law can not be applied in the case of a finite wire.As you have to notice that currnt cant just flow through a wire on its own .. it has to be connected to a part of a ciruit , so the magnetic field you are getting is the ttal field due to the entire system.

Anand Narayanan

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12 Aug 2011 20:03:38 IST

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But .... It is also the same case with infinite wire!! ??

sukhi

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3 Feb 2012 11:10:56 IST

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comparison Ampere circuital law and biot savart law

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