1.

State Ampere's circuital law and express it mathematically. Give the sign convention involved in the relation.

Answer»

Solution :Ampere.s circuital law states that for an open SURFACE with a boundary, the INTEGRAL of the product of tangential component of magnetic field for an element and the length of element is equal to `mu_0` times the total current PASSING through the surface.
Mathematically,
`oint B_t dl = oint vecB . vec(dl) = mu_0 I`
Where I is the current through the surface. the integral is taken over the closed loop coinciding with the boundary C of the loop.
As per sign convention followed, let the fingers of the right hand be CURLED in the boundary is traversed in the loop integral `oint vecB. vec(dl)`, then the DIRECTION of the given thumb gives the sense in which the current I is regarded as positive.


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