(hrwc31p98_6e) A solenoid is wound with a single layer of insulated copper wire

Question

(hrwc31p98_6e) A solenoid is wound with a single layer of insulated copper wire of diameter 2.700mmand has a diameter of 5.000cmand is 1.200mlong. Assume that adjacent wires touch and that insulation thickness is negligible.

A solenoid is wound with a single layer of insulated copper wire of diameter 2.700mmand has a diameter of 5.000cmand is 1.200mlong. Assume that adjacent wires touch and that insulation thickness is negligible. How many turns are on the solenoid? What is the inductance per meter (H/m) for the solenoid near its center?

Explanation / Answer

The inductance of a coil of wire is given by

L = µ N^2 A / l

A = cross-sectional area (diameter of 5.000 cm)
l length 1.2 m
µ =1.257 10^-6 (magnetic constant)

Solenoid length 190 cm with N= 633 turns,

Coil radius r = 2.7 mm gives area A =2.29E-5 m^2.

Relative permeability of the core k = 1

Then the inductance of the solenoid is

B =0.0005203 Henry =0.5203476 mH.

inductance per meter = L / 1.9

B =0.0002738 Henry/m =0.2738 mH/m

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