Solving with gyromagnetic ratio

Electricity and Magnetism Level pending

A conducting solid sphere of radius 1 meter and charge 1 coulomb is set rotating with constant angular speed 9 radians per second about its diameter axis . Find its magnetic moment ( in SI units).


The answer is 3.

Pranav Rao by Pranav Rao , 22, India

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1 solution

Pranav Rao
Nov 7, 2015

In this question we can use the gyromagnetic ratio which is Q/2m .But one has to be careful to use the moment of inertia of a spherical shell and not of Solid sphere as the sphere is conducting and all its charge resides on its surface.

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I don't think this is right. Moment of Inertia is a physical property related to mass distribution and is not governed by the distribution of charge on the body. The suggested solution would be right if the sphere were hollow and not solid. Why, otherwise, we would be using the same solution to explain conducting spheres with any pattern of mass distributions, which obviously ceases to be logical.

Gyromagnetic ratio = q/2m holds only when mass and charge distributions are identical.

Jaidev Ashok - 5 years, 3 months ago

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It is a shortcut actually.The answer can be also found out by integration. But most of us remember the formula for the moment of inertia for objects like hollow and solid spheres and these values can be used to solve the problem quickly.

Pranav Rao - 5 years, 2 months ago

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