In very dry weather, if you shuffle across the carpet wearing rubber-soled shoes and then bring your finger near a metal object such as a doorknob, you will probably get a shock and see a spark. How...

In very dry weather, if you shuffle across the carpet wearing rubber-soled shoes and then bring your finger near a metal object such as a doorknob, you will probably get a shock and see a spark. How this can occur is puzzling, since rubber is an insulator, so charge can't move through the soles of your shoes. Explain this process in detail, with appropriate diagrams. Make sure that you answer the following questions: (a) Carry out an experiment to determine the sign of the charge on the sole of your shoe after rubbing it on carpet, wool, or other cloth. Explain the test you did. (If you are unable to obtain results, choose a sign to use in the rest of the discussion.) (b) Draw a diagram that includes both the shoe and the rest of your body. Include all relevant charges and fields. (c) Suppose that a spark occurred when your finger was 1 cm from the doorknob. Draw two diagrams showing your hand, the doorknob, all relevant charges, and all contributions to the electric field at relevant locations: when your finger is 1.5 cm from the doorknob (no spark yet), and when your finger is 1 cm from the doorknob (spark starts). On the basis of these diagrams, explain why the spark starts only when your finger is close enough (1 cm) to the doorknob and not farther away. (d) At what location do you think the spark starts, and why (why not somewhere else)? (e) Why does the spark stop?