Final answer:
The ratio of the magnetic moments of the new coil and the original coil is 4:1.
Step-by-step explanation:
To calculate the ratio of the magnetic moments of the new coil and the original coil, we need to understand how the magnetic moment is related to the number of turns and the area of the coil.
The magnetic moment of a coil is given by the formula: M = NIA where N is the number of turns, I is the current, and A is the area of the coil.
In the given problem, the current 'I' remains the same, so we can ignore it when calculating the ratio of the magnetic moments.
Now, let's consider the area of the new coil. The original coil has a diameter 'd' and thus, a radius 'r'. So, its area is given by A = πr^2.
The new coil has a diameter '2d' and thus, a radius '2r'. So, its area is given by A' = π(2r)^2 = 4πr^2.
Therefore, the ratio of the magnetic moments is given by M'/M = A'/A = (4πr^2)/(πr^2) = 4.
Hence, the ratio of the magnetic moments of the new coil and the original coil is 4:1.