Question

10. A portion of a long cylindrical wire of radius R carries a current downward. The current density varies over the cross section of the wire such that J = ar where r is the distance from the center of the wire and a is a constant. (25 pts) A. What is the magnitude (in terms of Ra and wo) and direction of the magnetic field at a distance r from the center of the wire where r<R? dB - MI 47R² X B = Mo J 2tta KLI 47a² B-mar za B = cc 7 picturs? lined from? B. What is the magnitude (in terms of R. a and wo)and direction of the magnetic field for > R? dB-MI I X 233 477R? Bocca C. A square loop of wire R on a side carries a current in the clockwise direction, is placed adjacent to the wire with the near side a distance 1.5R from the center of the wire. What is the magnitude (in terms of Ra and po) and direction of the net force on the loop? Mo Izl 2 V

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Answer 1

given 0 = 320 Ti = 102N h = 12. 5m R = R=Radius Current densita J = del Consider an element of radius &. width dr. Current i= Joda = ds. 214.ds. is 2 8 .04. Cumente is daar sal from a ampesian Cincuital Law. B.L:Moi B. 27 e = Mox2 magnetic field = B = Mode? Answer. 2 do: 02 - Netcurrent in wire i dan from ampenian loop law. - B. 2 is r = MiD B.2T1 = Moa Els