3.Ampere's circuital law - Please explain the proof for a circular path ?

Asked by  | 19th Jun, 2009, 11:40: AM

Expert Answer:

Ampere's Circuital Law
Ampere's law is a useful relation that is analogous to Gauss's law. Ampere's law is a relationship between the tangential component of magnetic field at points on a closed curve and the net current through the area bounded by the curve.
 
Ampere's law is formulated in terms of the line integral of B around a closed path denoted by
 
We divide the path into infinitesimal segments dl and for each one calculate the scalar product of B and dl. In general, B varies from point to point and the B at the location of each dl must be used.
 
Consider a long straight conductor carrying a current passing through the centre of a circle of radius r in a plane perpendicular to the conductor.
 
Using Biot Savart's law we know already that the field at a distance r is the field at all points on the circle and the direction is given by  the tangent drawn to the circle at that point.
 
 
 
 
 
i.e., the flux is equal to the times the current threading through the area bounded by the circle. Hence, Ampere circuital law can be stated as follows
 
"The line integral of the magnetic field B around any closed path is equal to m0 times the net current across the area bounded by the path."
 
does not necessarily mean that B = 0 everywhere along the path, but only that no current is linked to the path.

Answered by  | 19th Jun, 2009, 08:41: PM

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