Solution Found!
A small segment of wire in FIGURE Q23.4 contains 10 nC of
Chapter 23, Problem 23.26(choose chapter or problem)
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 \(\lambda_{\mathrm{f}} / \lambda_{\mathrm{i}}\), where \(\lambda_{\mathrm{i}}\) 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?
Questions & Answers
QUESTION:
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 \(\lambda_{\mathrm{f}} / \lambda_{\mathrm{i}}\), where \(\lambda_{\mathrm{i}}\) 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?
ANSWER:
Step 1 of 6
Consider:
The original length of the wire is
The original charge on the wire is
(a). The initial linear charge density of the wire is,
When the length of the wire is shrunk to one third of the original length of the wire,
Thus, the final linear charge density of the wire (when the charge on the remain same) becomes,
