Question

I need help answering 18, 19, and 20. Thanks!

A wire is formed into a circle having a diameter of 18.0 cm and placed in a uniform magnetic field of 3.10 mT. The wire carries a current of 5.00 A. Find the maximum torque on the wire. Find the range of potential energies of the wire-field system for different orientations of the circle A long solenoid that has 1,180 turns uniformly distributed over a length of 0.440 m produces a magnetic field of magnitude 1.00 Times 10^-4 T at its center. What current is required in the windings for that to occur? A certain superconducting magnet in the form of a solenoid of length 1.00 m can generate a magnetic field of 10.0 T in its core when its coils carry a current of 55 A. The windings, made of a niobium-titanium alloy, must be cooled to 4.2 K. Find the number of turns in the solenoid.

Answer 1

18)a)τ= μ*B = NIABsinθ = 1*5.00*π*0.09^2*3.10*10^-3*sin90 = 0.4*10^-3 N.m

b) The energy of the system is given by U = − μ*B = − μBcosθ. The range of U depends on the fact that cos ranges between +1 and − 1. Hence the range of the potential energy is – 1.18* 10 ^− 4 J to1 .18 *10^ − 4 J

19) Magnetic field for the solenoid , B= μ₀NI/L

1*10^-4= (8.85*10^-12*I*1180)/(0.440)     => I = 4.2*10^3 A

c) Magnetic field for the solenoid , B= μ₀NI/L

10 = (8.85*10^-12*55*N)/(1.0)      => N=2.05*10^10 turns