The actual question was to somehow derive the expression for a magnetic field at the center of a current carrying loop.
The Biot-Savart's law equation
dB = (mu/4π)*(i dl x r)/r^3
(I'm not actually good at typing in the equations, so please just forgive me)
The Attempt at a Solution
Found an expression for the magnetic field due to a differential element at the centre and integrated it along the loop, and I got the expression.
Now, exactly coming to my point, is this derivation possible using Ampere's circuital law? If yes, how? If no, then what are the other situations except the cases of solenoid and toroid, where it is applicable? Please be brief and thanks in advance...