Respuesta :
The magnetic field strength is 9.47 ×10⁻⁴ T
The energy density at the center of the loop is 0.36 J/m³
Calculating Magnetic field strength & Energy density
From the question, we are to find the magnetic field strength
The magnetic field strength of a loop can be calculated by using the formula,
[tex]B = \frac{\mu_{0} I}{2R}[/tex]
Where B is the magnetic field strength
[tex]\mu_{0}[/tex] is the permeability of free space [tex](\mu_{0}=4\pi \times 10^{-7} \ N/A^{2})[/tex]
[tex]I[/tex] is the current
and R is the radius
From the give information,
[tex]R = 75 \ mm= 75 \times 10^{-3} \ m[/tex]
and [tex]I = 113 \ A[/tex]
Putting the parameters into the formula, we get
[tex]B = \frac{4\pi \times 10^{-7} \times 113}{2 \times 75 \times 10^{-3} }[/tex]
[tex]B = 9.47 \times 10^{-4} \ T[/tex]
Hence, the magnetic field strength is 9.47 ×10⁻⁴ T
Now, for the energy density
Energy density can be calculated by using the formula,
[tex]u_{B} = \frac{B^{2} }{2\mu_{0} }[/tex]
Where [tex]u_{B}[/tex] is the energy density
Then,
[tex]u_{B}= \frac{(9.47\times 10^{-4} )^{2} }{2 \times 4\pi \times 10^{-7} }[/tex]
[tex]u_{B} = 0.36 \ J/m^{3}[/tex]
Hence, the energy density at the center of the loop is 0.36 J/m³
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