Final answer:
The inductance L of the coil, calculated using the provided formula and the given measurements for radius and length, is 2,800 microhenrys. This value does not match any of the options provided in the question.
Step-by-step explanation:
The inductance L in microhenrys for a coil used by a ham radio operator can be determined by the formula provided in the question. Given the radius r is 2 inches and the coil's length l is 7 inches, we can plug these values into the equation L = r2 × 10 × l. We are not given any dependence of the inductance on the number of turns of wire, so this information is irrelevant for this calculation.
To solve for L, we convert inches to microhenrys to ensure consistent units:
- Radius r = 2 inches
- Length l = 7 inches
Substitute these values into the equation:
L = (2 inches)2 × 10 × (7 inches)
L = 4 × 10 × 7
L = 280 × 10
L = 2,800 microhenrys
Therefore, the inductance L of the coil is 2,800 microhenrys, but since none of the options given (a: 1,076.31, b: 1,056.41, c: 1,036.61, d: 1,046.51) matches this value, there might be a misunderstanding in the question or a possible typo in the options provided.