As shown in Figure P25.57, two large parallel vertical conducting plates separated by distance d are charged so that their potentials are +V0 and -V0. 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, so the potential of the ball is fixed at V = 0. The ball hangs straight down in stable equilibrium when V0 is sufficiently small. Show that the equilibrium of the ball is unstable if V0 exceeds the critical value ked2mg/(4RL).
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As shown in Figure P25.57, two large parallel vertical conducting plates separated by distance d are charged so that their potentials are +V0 and -V0. 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, so the potential of the ball is fixed at V = 0. The ball hangs straight down in stable equilibrium when V0 is sufficiently small. Show that the equilibrium of the ball is unstable if V0 exceeds the critical value ked2mg/(4RL).
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