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.
Sub Topics
Applications of Ampere Circuital Law
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In some cases of practical importance, symmetry considerations make it possible to use Amperes law to compute the magnetic field caused by a certain current carrying conductor.
Guidelines to use Amperes circuital law
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- If B is everywhere tangent to the integration path and has the same magnitude B at every point on the path, then its line integral is equal to B multiplied by the circumference of the path.
- If B is everywhere perpendicular to the path, for all or some portion of the path, that portion of the path makes no contribution to the line integral.
- In the integral
, 'B' is always the total magnetic field at each point on the path. In general, this field is caused partly by currents linked by the path and partly by the currents outside. Even when no current is linked by the path, the field at points on the path need not be zero - Two useful guiding principles to choose an integration path are that the point at which the field is to be determined must lie on the path and that the path must have enough symmetry so that the integral can be valuated easily.
