Consider the following magnetic potential expressed in spherical coordinates. k VM = (3 cos²0-1) (known as a quadrupolar potential). (a) If the magnetic field B=-VVM, then show that 3k B (3 cos²0-1)+ 6k sin cos 00. [Look up an expression for VV in spherical coordinates.] (b) Derive a simple value for the divergence of this magnetic field at all points in space [look up an expression for divergence in spherical coordinates]. (c) Show that the left-hand and right-hand sides of Gauss's theorem are equal for the case of vector field B and a sphere of radius 1 m, centred on the origin. [Hints: Calculate the total magnetic flux (B-dS) in/out of the sphere. The derivative of cos³ is -3 cos² 0 sin 0.]

Consider the following magnetic potential expressed in spherical coordinates. k VM = (3 cos²0-1) (known as a quadrupolar potential). (a) If the magnetic field B=-VVM, then show that 3k B (3 cos²0-1)+ 6k sin cos 00. [Look up an expression for VV in spherical coordinates.] (b) Derive a simple value for the divergence of this magnetic field at all points in space [look up an expression for divergence in spherical coordinates]. (c) Show that the left-hand and right-hand sides of Gauss's theorem are equal for the case of vector field B and a sphere of radius 1 m, centred on the origin. [Hints: Calculate the total magnetic flux (B-dS) in/out of the sphere. The derivative of cos³ is -3 cos² 0 sin 0.]

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter13: Nuclear Structure

Section: Chapter Questions

Problem 2Q: A proton precesses with a frequency p in the presence of a magnetic field. If the intensity of the...

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