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: A solenoid25cmlong and with a cross-sectional area of0.5cmcontains400turns of wire and carries a current of80A. Calculate: (a) the magnetic field in the solenoid; (b) the energy density in the magnetic field if the solenoid is filled with air; (c) the total energy contained in the coil’s magnetic field (assume the field is uniform); (d) the inductance of the solenoid.

Short Answer

Expert verified

a)B=0.161T

b)u=1.03×104J/m3

c)U=129mJ

d)L=4.02×10-5H

Step by step solution

01

The formulas used in the given problem

The magnetic field in a solenoid is given by B=μ0nI.

The energy stored in a solenoid is given by U=12LI2.

The energy density is given by B22μ0or it is simple energy per volume.

02

Calculate the magnetic field

The magnetic field is given by

B=μ0nIB=μ0NIlB=4π×10-7×400×800.25B=0.161T

03

Calculate the energy density

The energy density is given by

u=B22μ0u=0.16122×4π×10-7u=1.03×104J/m3

04

Calculate the total energy stored in the solenoid

The total energy can be given by the product of energy density and volume.

V=lAV=0.25×0.5×10-4V=1.25×10-5m3

The total energy will be

U=uVU=1.03×104×1.25×10-5U=129mJ

05

Calculate the self-inductance

The energy is given by U=12LI2. Use this formula to calculate the self-inductance.

L=2UI2L=2×0.129802L=4.02×10-5H

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