Problem — The comb and the paper

Problem

The comb and the paper. You rub a plastic comb on dry hair; brought close to small pieces of uncharged paper, the paper jumps up and sticks to it. (a) Why is the paper attracted if it is neutral? (b) Why does it only work with dry hair? (c) What if you wetted the comb with tap water? Discuss the mechanism of electrostatic induction in dielectrics.

Solution

(a) Attraction of a neutral body. By rubbing, the comb becomes charged (say, negatively). Brought close to the pieces of paper, which are insulators (dielectrics), it does not move free charges but polarises the molecules: in each molecule the charges shift slightly, forming small oriented dipoles. The side of the paper near the comb takes on charge opposite in sign to that of the comb, the far side the same sign. Since the force goes as $1/r^2$, the attraction on the near side (opposite sign) exceeds the repulsion on the far side:

$F \propto \frac{1}{r^2},\qquad r_{\text{near}} < r_{\text{far}} \;\Longrightarrow\; F_{\text{attr}} > F_{\text{rep}}$

Result: net attraction, and the pieces jump onto the comb despite being globally neutral.

(b) Why dry hair is needed. Rubbing charges the comb only if the surfaces are dry. Moisture forms a thin conducting water layer that dissipates the accumulated charge (it flows off towards the humid air or the hands): the comb does not stay charged and the effect does not occur.

(c) Comb wetted with tap water. Tap water contains ions and is conductive: wetting the comb, the accumulated charge flows away immediately. The comb discharges and no longer attracts the paper.

$\ev{\text{dielectric polarisation}\Rightarrow\text{attraction; moisture/conductive water discharges the comb}}$

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Topics: Elettrostatica Concepts: Carica elettrica · Dipolo elettrico