Final answer:
To calculate the total length of wire needed for the solenoid, determine the number of turns per length needed to achieve the magnetic field, then multiply by the circumference of the solenoid and its length.
Step-by-step explanation:
To construct a solenoid that meets the specifications of having a magnetic field of 2.5-kG (or 0.25 T, since 1 T = 104 G), we first need to find the required number of turns per unit length (n) using the formula for the magnetic field inside a solenoid, which is given by B = μ₀*n*I, where μ₀ is the permeability of free space (4π x 10-7 T*m/A), I is the current, and B is the desired magnetic field. Knowing that B = 0.25 T and I = 3.0 A, we can rearrange the formula to solve for n (n = B / (μ₀*I)).
Once we have the value of n, we can determine the total number of turns (N) by multiplying n by the length of the solenoid, and then we can calculate the total length of wire needed, considering one turn of wire wraps around the diameter of the tube. The length of each turn of wire around the tube will be equal to the circumference of the tube which is π*d, where d is the diameter. Therefore, the total length of wire is N times the circumference of the tube (N * π*d).