The energy density at the center of a circular loop of wire carrying a 23.0 a current if the radius of the loop is 28.0 cm will be 1.06 * [tex]10^{-3}[/tex] J / [tex]m^{3}[/tex]
Energy density is defined as the amount of energy accumulated in a system per unit volume. In the case of electrical energy. Electrical energy density = permittivity* Electric field squared/2 mu0
When an electric current is passed through a current-carrying circular wire loop, the magnetic field lines are generated in a circular pattern around the arms of the coil while the magnetic field lines are straight at the center of the loop
The magnetic field strength at the center of a circular loop is given by
B=(muo*I)/2R (at center of loop),
Energy density = [tex]B^{2}[/tex] / 2 (mu0)
= [tex]\frac{1}{2 (muo)}[/tex] * [tex](\frac{muo * I}{2R})^{2}[/tex] = [tex]\frac{muo * I^{2} }{8 * R^{2} }[/tex]
= [tex]\frac{4*3.14*10^{-7}*(23)^{2} }{8 * (0.28)^{2} }[/tex]
= 1.06 * [tex]10^{-3}[/tex] J / [tex]m^{3}[/tex]
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