Question

3. Infinite conductor a) Consider a straight conductor (infinite length) which carries a total current I in the direc- tion of the z axis. Calculate the magnetic induction Ē(7) using the Biot-Savart law. Hint The current density is given by j = 1S(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 = 407 c) Now, consider a second conductor of quadratic shape with size 2a that carries the current I. 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 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 conductor is infinitesimally thin, such that it can be described by a current thread. Write down the paramтetrization of the 4 linear parts of the conductor (for and calculate the corresponding integrals on the second closed conductor as a function of the angle p that torque density. Assume that the оver a arbitrary angle ) an

Answer 1

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