A solenoid is created by wrapping a L = 45 m long wire around a hollow tube of d

Question

A solenoid is created by wrapping a L = 45 m long wire around a hollow tube of diameter D = 15 cm. The wire diameter is d = 0.75 mm. The solenoid wire is then connected to a power supply so that a current of I = 65 A flows through the wire. L = 45 m D = 15 cm d = 0.75 mm I = 65 A Write an expression for the number of turns, N, in the solenoid. You do not need to take into account the diameter of the wire in this calculation. Calculate the number of turns, N, in the solenoid. Write an expression for the length of the solenoid (L_2) in terms of the diameter of the hollow tube D, the length of the wire L and the diameter of the wire d. Assume it is constructed by using only 1 layer of loops (note that most solenoids are actually constructed with many layers, to maximize the magnetic field density). Calculate the length of the solenoid (L_2) in meters. Calculate the magnitude of the magnetic field at the center of the solenoid in tesla.

Explanation / Answer

a)
let N be the turns
so we have
L = Nx pi x D
N = L/pi D
b)
N = 955 turns
c)
length of solenoid
L2 = N x d
L2 = (L/piD) x d
d)
L2 = 0.716m
e)
B = u N i /L
B = 1.733 x 10^-4 T

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