Respuesta :
Answer:
a) Energy density of the magnetic field, u = 183.46 J/m³
b) Total energy, E = 0.167 J
Explanation:
a) Number of turns in the solenoid, N = 1410
Area, A = 13.8 cm² = 0.00138 m²
Current, I = 8.01 A
Length of the solenoid, l = 66.1 cm = 0.661 m
Energy density, u is given by the formula [tex]u = \frac{B^2}{2 \mu_{0} }[/tex]
Where B is the magnetic field
The magnetic field in a solenoid is given by the formula, [tex]B = \frac{N \mu_{0} I }{l}[/tex]
[tex]B = \frac{1410 * 8.01* \mu_{0} }{0.661}[/tex]
[tex]B = 17086.38 \mu_0[/tex] T
[tex]u = \frac{(17086.38 \mu_0)^2}{2 \mu_{0} }\\u = \frac{291944527.29 \mu_0^2}{2 \mu_{0} }\\u = \frac{291944527.29 \mu_0}{2 }\\u = \frac{291944527.29 * 4\pi * 10^{-7} }{2 }\\u = 183.46 J/m^3[/tex]
b) The total energy = Energy density * Volume
E = u V
Volume = Area * Length
V = Al = 0.00138 * 0.661
V = 0.00091218 m³
E = 183.46 * 0.00091218
E = 0.167 J
