To solve this problem it is necessary to apply the concepts related to the energy density in the magnetic fields. Mathematically the expression that determines the relationship between the magnetic field, the permeability constant and the energy density is given by
[tex]u = \frac{B^2}{2\mu_0}[/tex]
Where,
B = Magnetic Field
u = Energy density in magnetic field
[tex]\mu_0[/tex]= Permeability constant
At the same time the energy of a given volume of space is given as
E = uV
Where
E = Magnetic field energy
V = Volume
Our values are given as
[tex]\mu_0 = 4\pi*10^{-7}Tm/A[/tex]
[tex]B = 4.8T[/tex]
[tex]V = 10cm^3 = 10*10^{-6}m^3[/tex]
Replacing in the first equation we can find the energy density
[tex]u = \frac{B^2}{2\mu_0}[/tex]
[tex]u = \frac{4.8^2}{2(4\pi*10^{-7})}[/tex]
[tex]u = 9.167*10^{6}J/m^3[/tex]
Now the net energy would be given by
[tex]E = uV[/tex]
[tex]E = (9.167*10^{6})(10*10^{-6})[/tex]
[tex]E = 91.67J[/tex]
Therefore the Magnetic Field energy is 91.67J
