Equivalence of a Magnetic Shell and Current Circuit

A current circuit may be considered to be equivalent to a magnetic shell whose boundary coincides with the circuit and whose strength is proportional to the current. This is the important of the concept of magnetic shell.

Consider a closed circuit ABCDA carrying a current i. divide the circuit into a large number of meshes such as abcda.

Let the same current i flow round each mesh in the same direction as in ABCDA.
Consider any one mesh abcda. The magnetic effect due to an equal and opposite current due to current flowing along any side of it is exactly cancelled by the magnetic effect due to an equal and opposite current due to the adjacent mesh. This applies to all meshes. The only effect current that remains is of strength I flowing round the circuit. Each small shell can be considered equivalent to a smalls circular current given a magnetic field equal to the one produced by a shell of same area. The combination of these small shells gives rise to a single shell of strength I whose boundary coincides with the circuit ABCDA. Thus the current circuit can be replaced by a magnetic shell of the same boundary and the effect is same if the strength of the shell is equal to the strength of the current.
The concept can be used for calculating the magnetic effects produced by the electrical circuits especially which are of irregular shape.

Ampere’s Theorem

“A current flowing in any closed circuit produces the same magnetic effect in its neighborhood as an equivalent magnetic shell whose boundary coincides with the conductor through which the current flows, the strength of the current being equal to the strength of the shell”.



For more help in Equivalence of a Magnetic Shell and Current Circuit  please click the button below to submit your homework assignment