Open-Response Homework Problem 18.2 The sewer pipe solenoid you used in lab to m
ID: 1461082 • Letter: O
Question
Open-Response Homework Problem 18.2 The sewer pipe solenoid you used in lab to measure the earth?s magnetic field had 79 turns wound on 79cm. It?s diameter is 4in (1in = 2.54cm). (a)[3 pt(s) Compute the self-inductance. (b)[2 pt(s) Compute the magnetic energy (ignoring the earth?s field) if 0.25A flows through the solenoid. (c)[2 pt(s) Compute the magnetic energy density by dividing the energy by the volume of the solenoid. (d)[1 pt(s) Compare the result in (c) with the result found from the formula for magnetic energy density.Explanation / Answer
a.
inductance of solenoid is given by:
L = miuo*N^2*A/l
l = 79 cm = 0.79 m
A = pi*r^2 = pi*(2*2.54*10^-2)^2 = 8.107*10^-3 m^2
L = miuo*N^2*A/l
= (1.2566*10^-6)*(79)^2*( 8.107*10^-3 )/(0.79)
= 8*10^-5 H
Answer: 0.8 H
b.
E = 0.5*L*i^2
= 0.5*8*10^-5* (0.25)^2
= 2.5*10^-6 J
Answer: 2.5*10^-6 J
c.
Volume = A*l
= 8.107*10^-3 * 0.79
= 6.4*10^-3 m^3
Energy density = E/Volume
= (2.5*10^-6)/(6.4*10^-3)
= 3.9*10^-4 J/m^3
d.
B = N*miuo*I/length= 79*1.2566*10^-6*0.25/0.79 = 3.14*10^-5 T
Energy density = 0.5*B^2/miuo
= 0.5*(3.14*10^-5 )^2 / (1.2566*10^-6)
= 3.9*10^-4 J/m^3
Both are equal
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