Final answer:
The magnetic moment of a current carrying a circular coil with radius R and N turns is given by μ = NIπR², showing that it directly varies as the product of N and I. Thus, the magnetic moment varies as NI. The options provided do not accurately reflect this; the closest one is 'NR/I', but this incorrectly suggests an inverse relationship with the current.
Step-by-step explanation:
The magnetic moment (μ) of a current (I) carrying a circular coil of radius (R) and number of turns (N) is given by the product of the current, the number of loops, and the area of the loop. So, the magnetic moment μ is given by:
μ = NIA
Where A is the area of the loop (πR² for a circular loop). Thus, we can see that the magnetic moment varies as:
μ = NIπR²
This suggests that the magnetic moment varies with the product of the number of turns (N) and the current (I), but is also proportional to the square of the radius (R). So, the correct relationship considering the constants would be:
μ ∝ NR²I
However, if we simplify this to just show the direct relationship with each of the variables listed, ignoring the constants and the square of the radius for direct proportionality, the magnetic moment varies as:
μ ∝ NI
From the given options the closest one is (d) NR/I, although this appears to incorrectly include an inverse relationship with the current that is not actually present in the equation for magnetic moment.