let us study about calculation of magnetic
induction due to a straight wire using amp ere’s law . say if we are given with a straight
wire, which carries a current-I, and due to this wire, at a distance r from it, at a point
p, we are required to find, the magnetic induction . here, by applying amp ere’s law .
on a closed path, which we consider as a circle of radius-r , with centre at point-o , we
can calculate, the magnetic induction, and for the same we consider here a small element
of length dl on this path , say the name of path we write as m.
and, from the wire it is at a distance-r, as magnetic field exist in the direction tangential
to the wire the angle between magnetic induction and the element length dl is 0, so here we
can use. by applying . amp ere’s law . on path m , here we can see it is integration
for closed path m it is b dot dl , is equal to mu knot times the total current passing
through the enclosed area which is here I, this b dot dl we can write as b dl because
the angle between the 2 is 0 . so it is integration of b dl is mu knot I,
and we know at distance r the magnetic induction remains uniform by symmetry , so here, this
b can be taken out of this integration sign , so it is integration of dl , for path m.
is mu knot I, and for the whole path integral for this elemental length dl is the sircumference
of the path , which is b multiplied by 2 pie r, is mu knot- I, so here the value of this
magnetic induction we can write as , mu knot-I by 2 pie r.
here we can see we have obtained the magnetic induction at point p due to wire , with a
simple calculation using am pair’s law , whereas in the previous section we have calculated
the same result using bio sauvart’s law by using long integral, that is why , we write
that, amp ere’s law , is helpful in symmetric uniform current distribution. in cases of
calculation of magnetic induction.