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## Homework Statement

The actual question was to somehow derive the expression for a magnetic field at the center of a current carrying loop.

## Homework Equations

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

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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...