Chapter 23, Problem 4CQ

A small segment of wire in FIGURE Q23.4 contains 10 nC of charge.

a. The segment is shrunk to one-third of its original length. What is the ratio ${\lambda }_f/{\lambda }_i$ , where ${\lambda }_i$ and ${\lambda }_f$ are the initial and final linear charge densities?

b. A proton is very far from the wire. What is the ratio $F_f/F_i$ of the electric force on the proton after the segment is shrunk to the force before the segment was shrunk?

c. Suppose the original segment of wire is stretched to 10 times its original length. How much charge must be added to the wire to keep the linear charge density unchanged?