The magnetic flux density at a point due to a current-carrying coil is determined by Ampere's Law.

Explanation:

Ampere's Law is one of the four Maxwell's equations that describe the behavior of electric and magnetic fields. It relates the magnetic field surrounding a closed loop to the electric current passing through the loop.

Mathematically, Ampere's Law is given by:

∮B.dl = μ0I

where ∮B.dl is the line integral of the magnetic field B around a closed loop, μ0 is the permeability of free space, and I is the electric current passing through the loop.

The above equation states that the magnetic flux density (B) at a point due to a current-carrying coil is directly proportional to the electric current passing through the coil. The law also states that the magnetic field lines form closed loops around the current-carrying conductor.

The law can be applied to a current-carrying coil by considering the coil as a series of current-carrying loops. The magnetic field at a point due to each loop can be calculated using the Biot-Savart Law. The total magnetic field at the point is then obtained by summing up the contributions from all the loops using Ampere's Law.

In summary, Ampere's Law is used to determine the magnetic flux density at a point due to a current-carrying coil. It relates the magnetic field surrounding a closed loop to the electric current passing through the loop. By applying the law to a current-carrying coil, the magnetic field at a point can be calculated by summing up the contributions from all the loops.