CBSE Class 12-science Answered
3.Ampere's circuital law - Please explain the proof for a circular path ?
Asked by | 19 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 | 19 Jun, 2009, 08:41: PM
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