Answer with Explanation:
We are given that
Length of solenoid,l=82.4 cm=[tex]\frac{82.4}{100}=0.824 m[/tex]
1m=100 cm
Area,A=[tex]23.0 cm^2=23\times 10^{-4} m^2[/tex]
[tex]1cm^2=10^{-4} m^2[/tex]
Number of turns,N=1380
Current,I=5.89 A
a.Magnetic field of solenoid,[tex]B=\frac{\mu_0 NI}{l}[/tex]
Where [tex]\mu_0=4\pi\times 10^{-7}[/tex]
Using the formula
[tex]B=\frac{4\pi\times 10^{-7}\times 5.89\times 1380}{0.824}=0.0124 T[/tex]
Energy density of the magnetic field inside the solenoid=[tex]u=\frac{B^2}{2\mu_0}=\frac{(0.0124)^2}{2\times 4\pi\times 10^{-7}}=61.2 J/m^3[/tex]
b.Total energy stored in the magnetic field=[tex]u(Al)=61.2\times (23\times 10^{-4}\times 0.824=115.9\times 10^{-3} J=115.9 mJ[/tex]
[tex]1mJ=10^{-3} J[/tex]
