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Problem Consider a circular loop of wire of radius R located in the yz plane and carrying a steady current I as in Figure 30.6. Calculate the magnetic field at an axial point Pa distance x from the center of the loop. Strategy In this situation, note that any element os is perpendicular to f. Thus, for any element, Jas x f| = (ds)(1)sin 90° = ds. Furthermore, all length elements around the loop are at the same distancer from P, where r2 = x2 + R2. dB, AB, Figure 30.6 The geometry for calculating the magnetic field at a point P lying on the axis of a current loop. By symmetry, the total field B is along this axis.

Problem Consider a circular loop of wire of radius R located in the yz plane and carrying a steady current I as in Figure 30.6. Calculate the magnetic field at an axial point Pa distance x from the center of the loop. Strategy In this situation, note that any element os is perpendicular to f. Thus, for any element, Jas x f| = (ds)(1)sin 90° = ds. Furthermore, all length elements around the loop are at the same distancer from P, where r2 = x2 + R2. dB, AB, Figure 30.6 The geometry for calculating the magnetic field at a point P lying on the axis of a current loop. By symmetry, the total field B is along this axis.

College Physics
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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Example 30.3 Magnetic Field on the Axis of a Circular Current Loop Problem Consider a circular loop of wire of radius R located in the yz plane and carrying a steady current I as in Figure 30.6. Calculate the magnetic field at an axial point Pa distance x from the center of the loop. Strategy In this situation, note that any element as is perpendicular to f. Thus, for any element, |ds × f| = (ds)(1)sin 90° = ds. Furthermore, all length elements around the loop are at the same distance r from P, where r² = x2 + R2. dB, AB, Figure 30.6 The geometry for calculating the magnetic field at a point P lying on the axis of a current loop. By symmetry, the total field B is along this axis.
Transcribed Image Text:Example 30.3 Magnetic Field on the Axis of a Circular Current Loop Problem Consider a circular loop of wire of radius R located in the yz plane and carrying a steady current I as in Figure 30.6. Calculate the magnetic field at an axial point Pa distance x from the center of the loop. Strategy In this situation, note that any element as is perpendicular to f. Thus, for any element, |ds × f| = (ds)(1)sin 90° = ds. Furthermore, all length elements around the loop are at the same distance r from P, where r² = x2 + R2. dB, AB, Figure 30.6 The geometry for calculating the magnetic field at a point P lying on the axis of a current loop. By symmetry, the total field B is along this axis.
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