It is desired to construct a solenoid that has a resistance of2.86 (at 20 degree

Question

It is desired to construct a solenoid that has a resistance of2.86 (at 20 degree C) and produces a magnetic field at itscenter of 0.0413 T when it carries a current of 1.04 A. Thesolenoid is to be constructed from copper wire having a diameter of1.12mm. The resistivity of the copper is 1.7x10^(-8).m. Find thenumber of turns of wire needed if the radius of the solenoid is tobe 0.52cm and find the length of the solenoid in cm The resistivity of the copper is 1.7x10^(-8).m. Find thenumber of turns of wire needed if the radius of the solenoid is tobe 0.52cm and find the length of the solenoid in cm

Explanation / Answer

        Given that theresistance of wire is R = 2.86         The magnetic field atcenter is B = 0.0413 T         Current is I = 1.04A         Diameter of wire is d =1.12*10-3m         Resistivity of copper is = 1.7*10-8 .m         radius of solenoid is r= 0.52cm =0.0052 m -----------------------------------------------     The resistance of wire is R = L/ A       = L /(d/2)2                                         L = R*(d/2)2 /                                             = -------- m     The magnetic field at the center of the solenoidis B = o*N*I / L                                                                         N = B*L / o*I                                                                               = --------- turns      The length of solenoid is l = N /2r                                          = -------- m

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