It is desired to construct a solenoid that will have a resistance of 4.10 Ohm (a

Question

It is desired to construct a solenoid that will have a resistance of 4.10 Ohm (at 20 degree C) and produce a magnetic field of 4.00 times 10^-2 T at its center when it carries a current of 5.00 A. The solenoid is to be constructed from copper wire having a diameter of 0.500 mm. If the radius of the solenoid is to be 1.00 cm, determine the following. (The resistivity of copper at 20 degree C is 1.7 times 10^-8 Ohm middot m.) the number of turns of wire needed to build the solenoid turns the length the solenoid should have cm

Explanation / Answer

a) r = d / 2 = 0.50 mm /2 = 0.25 * 10-3 m

R = p L / A , L = R (pi r2) / p

L = (4.10 * pi * (0.25 * 10-3)2) / (1.7 * 10-8) = 47.35 m

Number of turns = L / 2 pi r = 47.35 / (2 pi * 1 * 10-2) = 754 turns

b) n = B / mu0 I = (4.00 * 10-2) / (4 pi * 10-7 * 5) = 6366 turns/m

n = N / L

L = 754 / 6366 = 11.8 cm

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