Final answer:
The energy in the magnetic field of a solenoid is determined using the energy density formula and the volume of the solenoid. Once computed, it yields the total energy stored in the magnetic field.
Step-by-step explanation:
The question is asking for the energy stored in the magnetic field of an air-filled solenoid with certain dimensions and a given magnetic field strength. To find this energy, we need to use the formula for the energy density in a magnetic field, which is u = (B²)/(2μ₀), where u is the energy density, B is the magnetic field strength, and μ₀ is the permeability of free space (which is approximately 4π x 10⁻⁷ T·m/A).
Once we have the energy density, we can calculate the total energy stored in the magnetic field by multiplying the energy density by the volume of the solenoid's interior. The volume V of the solenoid can be found using the formula V = πr²h, where r is the radius of the solenoid and h is its height.
Given the data in the question, we can substitute the known values to find the answer. However, the exact numerical solution will depend on the specific numbers provided for the dimensions of the solenoid and the magnetic field strength.