Final answer:
To calculate the magnetic-field energy in the volume provided, the energy density formula u = ½ B²/μ₀ is used, and then this energy density is multiplied by the volume of the space.
Step-by-step explanation:
The question pertains to the calculation of magnetic-field energy stored in a given volume when a uniform magnetic field is present. The magnetic-field energy density (energy per unit volume) can be obtained using the formula u = ½ B²/μ₀, where u is the energy density, B is the magnetic field strength, and μ₀ is the permeability of free space (μ₀ = 4π x 10⁻⁷ T⋅m/A). In this scenario, the volume (V) is 13.0 cm³ (which is 13.0 x 10⁻⁶ m³), and the magnetic field strength (B) is given as 2.40 T. To find the total magnetic-field energy (E), multiply the energy density by the volume (E = uV).
First, we calculate the energy density:
u = ½(2.40 T)²/(4π x 10⁻⁷ T⋅m/A)
Then, multiply the energy density by the volume:
E = u * 13.0 x 10⁻⁶ m³
After doing the calculations, we find the total magnetic-field energy in the specified volume.