A Treatise On Electricity And Magnetism

Cover A Treatise On Electricity And Magnetism
A Treatise On Electricity And Magnetism
Maxwell James Clerk
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If, on the other hand, this quantity is negative, the force will tend to increase r, and the equilibrium will be unstable.
Now consider a sphere whose centre is the origin and whose radius is r, and so small that when the point fixed in the body lies within this sphere no part of the moveable body A can coincide with any part of the external system B, Then, since within the sphere V^M = 0, the surface-integral taken over the surface of the sphere, is zero.
Hence, if at any part of the surface o
...f the sphere dM/dr is positive, there must be some other part of the surface where it is negative, and if the body A be displaced in a direction in which dM/dr is negative, it will tend to move from its original position, and its equilibrium is therefore necessarily unstable.
The body therefore is unstable even when constrained to move ir-.
Digitized by Google 1 1 6.] EQUILIBBIUM ALWAYS UNSTABLE. 163 parallel to itself, and ^ fortiori it is unstable when altogether free.
Now let us suppose that the body A is a conductor.


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