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## Homework Statement

Consider a string of N beads connected by N-1 rigid rods of length l. The system is considered as one-dimensional with rods only being aligned either up or down. The string is immersed in a fluid at temperature T and first bead is fixed at the origin y=0. A constant electric field is applied in the positive y direction.

What is the average length of the string if

**only the last**bead holds a charge q.

## Homework Equations

[tex]\sum\frac{e^{-\beta E}}{Z} [/tex]

## The Attempt at a Solution

I'm a little unsure about how to consider the effects of the charged bead in the field.

My thoughts in general were to consider the rods in two states, either aligned with or against the field. If aligned with the field the energy is negative [itex]-eEl[/itex]. If aligned with the field the energy is positive [itex]+eEl[/itex]. By considering these states I hope to determine the probability of a rod being aligned with/against field and from that determine the expectation value of the length.

One one hand if only the end bead is charged only that bead will show a preferential alignment and the rest will be random.

On the other hand; if the Nth bead feels a force due to the applied field it will also apply a force to the N-1th bead, which will apply the force to the N-2th bead etc. In that way the work will be applied to all of the rods so the energy shift will apply to all beads.

Which is right? Or am I completely off-base?