Ampere's law provides us an easy way to calculate the magnetic field due to a symmetrical distribution of current. Its mathematical expression is `ointvecB.dl=mu_0I_("in")`.
The quantity on the left hand side is known as line as integral of magnetic field over a closed Ampere's loop.
Only the current inside the Amperian loop contributes in

Options

A. finding magnetic field at any point on the Ampere's loop
B. line integral of magnetic field
C. in both of the above
D. in neither of them

Answer

B

Explanation

(b)
Magnetic field at any point on Ampere's loop can be due to
all currents passing through inside or outside the loop. But net
contribution in the left hand side will come from inside current only.
For rlta, current passing through within the cylinder of radius
r is given by
`int_0^rJdA=int_0^rkr^2 2pirdr=2pikint_0^r r^3dr`
`=kpir^4//2`
Now using Ampere's law:
`Bxx2pir=mu_0I=mu_0kpir^4//2 implies B=(mu_0kr^3)/4`