Problem 4 As shown below, a wire of length L - 18.0 cm carries a current i 58.2 mA (a) Use the Biot-Savart law to find the magnitude of the magnetic field at point P, a distance R = 13.1 cm from the wire and halfway along the wire. (b) Check your answer to part (a) by considering the following opposite limits: (i) If the wire is very long relative to the distance of point P from it, ie, L 》 R, then the field should approach the field of an infinitely long straight wire. Is the expression for the magnetic field you derived in part (a), evaluated for L R, consistent with this prediction? (i) If point P is very far from the wire compared to the wire's length, i.e., R»L, we expect the field to be that of a very small (in the limit even infinitesimal) current element, and we expect to directly recover the Biot-Savart law, with L playing the role of ds. Is the expression for the magnetic field you derived in part (a), evaluated for L > R, consistent with this prediction?

Problem 4 As shown below, a wire of length L - 18.0 cm carries a current i 58.2 mA (a) Use the Biot-Savart law to find the magnitude of the magnetic field at point P, a distance R = 13.1 cm from the wire and halfway along the wire. (b) Check your answer to part (a) by considering the following opposite limits: (i) If the wire is very long relative to the distance of point P from it, ie, L 》 R, then the field should approach the field of an infinitely long straight wire. Is the expression for the magnetic field you derived in part (a), evaluated for L R, consistent with this prediction? (i) If point P is very far from the wire compared to the wire's length, i.e., R»L, we expect the field to be that of a very small (in the limit even infinitesimal) current element, and we expect to directly recover the Biot-Savart law, with L playing the role of ds. Is the expression for the magnetic field you derived in part (a), evaluated for L > R, consistent with this prediction?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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