A 1700-turn solenoid has a cross-sectional area equal to 8.0 cm2 and a length eq

Question

A 1700-turn solenoid has a cross-sectional area equal to 8.0 cm2 and a length equal to 30 cm. The solenoid carries a current of 4.0 A.

(a) Calculate the magnetic energy stored in the solenoid using U = ½ LI2, where L = 0n2A.

_____mJ

(b) Divide your answer in part (a) by the volume of the region inside the solenoid to find the magnetic energy per unit volume in the solenoid.

_____kJ/m3

(c) Check your Part (b) result by computing the magnetic energy density from um = B2/(20) where B = 0nI.

_____kJ/m3

Explanation / Answer

(a)

L = 0n2A.

=4*pi*10^-7*(1700)^2*8*10^-4*30*10^-2

=8.71*10^-4 H

Current I =4 A.

Hence magnetic energy,

= 1/2*L*I^2

=(1/2)*8.71*10^-4*4^2 =6.968 mJ.

(b) Mahneic enegy per volume,

= 6.968 mJ/Al

= 6.968 *10^-3/8*10^-4*30*10^-2

=0.029 kJ/m^3

(c) Magnetic field,

B =  0nI = 4*pi*10^-7*1700*4

=8.54*10^-3 T

Um = B^2/(20) =(8.54*10^-3)^2/2*4*pi*10^-7

=0.029 kj/m^3

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