Final answer:
The magnetic field at the centre of a circular coil is directly proportional to the magnitude of the current passing through it, as given by the formula B = μ_0I/(2R), making the correct option (d).
Step-by-step explanation:
The magnetic field produced at the centre of a circular coil is directly proportional to the magnitude of the current passing through it.
This is represented by the formula for the magnetic field strength at the center of a circular loop which is given as B = μ_0I/(2R), where μ_0 is the permeability of free space, I is the current, and R is the radius of the loop.
The result shows that the magnetic field is independent of the time for which the current is passed, the resistance of wire, and the radius of the loop in terms of direct proportionality. Therefore, the mentioned correct option in the final answer is (d) magnitude of the current passing through it.