Question

a long wire with a square cross-section 13 cm on a side carries a current of 10 a that is uniformly distributed over the cross-section of the wire. what is the value of the integral along a square with side length 8 cm concentric with the wire and with sides parallel to those of the wire?

Answer 1

The value of the integral along a square with side length 8 cm concentric with the wire and with sides parallel to those of the wires 4.7*10^-6 I-m.

The integral around a closed path of the component of the magnetic field tangent to the direction of the path equals µ0 times the current intercepted by the area within the path.

§ B.ds=UoI

Thus the line integral (circulation) of the magnetic field around some arbitrary closed curve is proportional to the total current enclosed by that curve.

Ampere’s Law can be useful when calculating magnetic fields of current distributions with a high degree of symmetry (similar to symmetrical charge distributions in the case of Gauss’ Law)

The total magnetic circulation is zero only in the the enclosed net current is zero, the magnetic field is normal to the selected path at any point the magnetic field is zero.

According to the amperes law,

§ B.ds=UoI

I is the current through Amperian loop

So,here I= A² Io/Ao^2 (as current is uniformly distributed)

              = 8^2*10/13*13 = 3.79A

§ B.ds=UoI

         = 4π*10^-7*3.79

         = 4.7*10^-6 I-m

To know more about ampere's law here

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