Question

If a cat repeatedly rubs against your cotton slacks on a dry day, the charge transfer between the cat hair and the cotton can leave you with an excess charge of $\mathbf{-}\mathbf{2}\mathbf{.00}\mathbf{\text{μC}}$.

(a) How many electrons are transferred between you and the cat?

You will gradually discharge via the floor, but if instead of waiting, you immediately reach toward a faucet, a painful spark can suddenly appear as your fingers near the faucet.

(b) In that spark, do electrons flow from you to the faucet or vice versa?

(c) Just before the spark appears, do you induce positive or negative charge in the faucet?

(d) If, instead, the cat reaches a paw toward the faucet, which way do electrons flow in the resulting spark?

(e) If you stroke a cat with a bare hand on a dry day, you should take care not to bring your fingers near the cat’s nose or you will hurt it with a spark. Considering that cat hair is an insulator, explain how the spark can appear.

Short answer

1. $1.25\times {10}^{13}\text{electrons}$are transferred.
2. The electrons “leap” from you to the faucet.
3. The faucet becomes positively charged just before the spark appears.
4. The flow of charge (electrons) is from the faucet to the cat.

Step-by-step solution

Given

Excess charge =$-2.00\text{\hspace{0.17em}μC}$

Understanding the concept

Charges are quantized. It means the charge on any object is equal to the integer multiple of an elementary charge. The charge will always be present in an integer number and never as a fraction.

(a) Calculate how many electrons are transferred between you and the cat

The number of electrons transferred is calculated asfollows:

$\begin{array}{c}\mathrm{n}=\frac{\left|\mathrm{q}\right|}{\mathrm{e}}\\ =\frac{(2.00\times {10}^{-6}\mathrm{C})}{(1.6\times {10}^{-19}\mathrm{C})}\\ =1.25\times {10}^{13}\text{electrons}\end{array}$

(b) Explain if the electrons flow from you to the faucet or vice versa

Since you have the excess electrons (and electrons are lighter and more mobile than protons), the electrons “leap” from you to the faucet instead of protons moving from the faucet to you (in the process of neutralizing your body).

(c) Find out if you induce a positive or negative charge in the faucet just before the spark appears

Unlike charges attract, and the faucet (which is grounded and is able to gain or lose any number of electrons due to its contact with Earth’s large reservoir of mobile charges) becomes positively charged, especially in the region closest to your (negatively charged) hand, just before the spark.

(d) If, instead, the cat reaches a paw toward the faucet, find out which way the electrons flow in the resulting spark.

The cat is positively charged (before the spark), and by the reasoning given in part (b),the flow of charge (electrons) is from the faucet to the cat.

(e) Explain how the spark can appear

If we think of the nose as a conducting sphere, the side of the sphere closest to the fur is of one sign (charge), and the side furthest from the fur is of the opposite sign (which, additionally, is oppositely charged from your bare hand that had stroked the cat’s fur). The charges in your hand and those of the furthest side of the “sphere” attract each other and, when close enough, manage to neutralize (due to the “jump” made by the electrons) in a painful spark.