Question

a) Consider a straight conductor (infinite length) which carries a total curremt I in the direc- tion of the z axis. Calculate the magnetic induction B(7) using the Biot-Savart law. Hint The current density is given by j = I8(x)6(y)ë^ b) Explicitly check the result from the previous task by calculating the magnetic induction B(F) using the symmetry of the problem and applying Stoke's theorem onto Maxwell's equation of magnetostatics V x B = HoJ. c) Now, consider a second conductor of quadratic shape with size 2a that carrics the current 2. This conductor is fixed at the center on an axis parallel to the first conductor at a distance d, see drawing 2a 2a Calculate the torque M on the second closed conductor as a function of the angle p that fixes the direction of the plane in which the second conductor lies. Evaluate your result for a d. Which angle do you get for the equilibrium position? Hint: The total torque is given by the integral over a torque density. Assume that the conductor is infinitesimally thin, such that it can be described by a current thread. Write down the parametrization of the 4 linear parts of the conductor (for an arbitrary angle p) and calculate the corresponding integrals.

Answer 1

is to otar Megnered a.) cue to mfinetylong stright eurrent wire let be 4u Pomt P A Curreut ekeuout and be tw osition veetor d augle betueou aud According o Biot-Savatd's law, 3 Tdlsmo &2 0- mas Eia (40-6)=Ces 2= atan And Cesdo Li ite For wire be Cs Scanned with CamScanner

Let The four curreut PQ,R, RSano SP 3 h Con a Snoon nm tw diagram a2ms clue to Cuinut B-LUTre 2.T1d amyuin O(180- cquedand opesite huy cancef F au trut eash the (PRXB IFJ-Ta)B uieatifom These turofores aunvng dffeseunt I (2a)B ga los d て Scanned with CamScanne CS