Electric Potential (w/ a pendulum :P)

[AgPIper]

Two large parallel vertical conducting plates separated by distance d are changed so that their potentials are (+V sub 0) and (-V sub 0).

A small conducting ball of mass m and radius R (where R<<d) is hung midway between the plates.

The thread of length L supporting the ball is a conducting wire connected to ground (at V=0)

The ball hands straight down in stable equilib when V sub 0 is sufficiently small.

Show that the equilib of the ball is unstable if V sub 0 exceeds the critical value k*d^2*mg/(4RL)

(Hint: consider the forces on the ball when it is displaced a distance x<<L.)

Thanks very much for answering! :-)

 

[JohnDubYa]

If the net force on an object points points away from a particular point in space as you move slightly away from that point in space, then the object is in a position of instability. Stable equilibrium requires that the net force re-directs the object back to its original point in space.

Consider a bowl with a mound in the middle of it. If a ball is placed perfectly at the top of the mound, it is in a position of unstable equilibrium. Why? Well, if the ball moves away from the top of the mound, the net force acting on the ball points away from the top of the mound.

Now ask the same question about a ball in the bottom of a perfectly shaped bowl with no mound.

 

[AgPIper]

thanks, though...

I now get the equilibrium concept, but still not sure about the free body diagram of the metal ball pendulum...