Final answer:
To calculate the energy stored in the magnetic field inside a cylindrical volume, first calculate volume using πr²h, then use the energy density formula u=B²/(2µ₀), and multiply by the volume to get the energy in joules.
Step-by-step explanation:
The student is asking how to calculate the energy stored in a magnetic field within a cylindrical volume. To find this, we use the formula for the energy density u in a magnetic field, which is u = B2 / (2µ0), where B is the magnetic field strength and µ0 is the permeability of free space. The permeability of free space (µ0) is a constant, valued at 4π x 10-7 T·m/A.
First, we calculate the volume of the cylinder using the formula V = πr2h, with r representing the radius and h the height (length) of the cylinder. Using the given radius of 1.82 cm (0.0182 m) and length of 24.6 cm (0.246 m), we find the volume V. Then, we use the magnetic field strength of 49.9 mT (0.0499 T) to calculate the energy density and multiply it by the volume to get the total energy stored in the magnetic field within the cylinder, giving the answer in joules. To convert to millijoules, multiply the result by 1000.
The total energy E stored in the magnetic field can be calculated using the formula:
E = uV = · (· 1.82 cm² · 24.6 cm) · 49.9 mT² / (2 · 4π · 10-7 T·m/A)