Question

Two conducting cylindrical wires with a diameter of 3 cm and length of 40 cm are made from a metal with a density of 2710 kg/m'. The wires carry equal but opposite current (the direction given in the diagram) of 7.5 amps and are suspended from a thread of length 25 cm and are 12 cm apart from each other. An external uniform magnetic field of magnitude 3.0 Tesla is applied to the system. A) Calculate the net magnetic field at wire 1 due to the magnetic field generated by wire 2 and the external magnetic field (5 points) B) Calculate the net magnetic field at wire 2 due to the magnetic field generated by wire 1 and the external magnetic field (5 points) C) Calculate the magnitude of the tension force in the thread for wire 1 (5 points) D) Calculate the angle θ created by the two threads (5 points) E) Calculate the net magnetic field at the point A which is 1/3 of the distance (L) between wire 1 and wire 2 (5 points) Wire 1 Wire 2

Answer 1

(a) B on wire 1 due to wire 2 B_21 = mu_0/4 pi 2I times V_21^bar/(r_21)^2 B_21 = 10^-7 times 2 times 7 times (-c^bar) times (-1^bar)/(L)^2 L rightarrow Vertical-bar r_21^vector Vertical-bar therefore B_21 = 15/L times 10^-7 j^^B to rl = [15 times 10^-7 + 3] j^^Tesla (b) therefore B_12 = B_21/2 therefore B_total = B_12 + 3 B_total = (15 times 10^-7/2L + 3]j^^Tesla (c) Mass = density times volume \r\n value of cylinder = pi r^2 L sigma f_y = 0 implies T cos theta/2 = Mg sigma F_x = 0 implies T sin theta/2 = Fm tan theta/2 = L/squareroot 0.25 - L^2 implies FM = Il times B therefore Form theta/2 = FM/Mg L^2 = 1.4(0.25 - L^2) implies L = 0.38 M Put L in (1), we get theta = 100 degrees T = Mg/cos 50 degrees = 11.9 N = T d) = tan theta/2 = L/squareroot 0.25 - L^2 = 0.38/squareroot 0.25