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A plastic rod with linear charge density l is bent into
Chapter 23, Problem 23.85(choose chapter or problem)
A plastic rod with linear charge density l is bent into the quarter circle shown in FIGURE P23.48. We want to find the electric field at the origin. a. Write expressions for the x- and y-components of the electric field at the origin due to a small piece of charge at angle u. b. Write, but do not evaluate, definite integrals for the x- and y-components of the net electric field at the origin. c. Evaluate the integrals and write E u net in component form
Questions & Answers
QUESTION:
A plastic rod with linear charge density l is bent into the quarter circle shown in FIGURE P23.48. We want to find the electric field at the origin. a. Write expressions for the x- and y-components of the electric field at the origin due to a small piece of charge at angle u. b. Write, but do not evaluate, definite integrals for the x- and y-components of the net electric field at the origin. c. Evaluate the integrals and write E u net in component form
ANSWER:Problem 23.85
A plastic rod with linear charge density l is bent into the quarter circle shown in Figure P23.48. We want to find the electric field at the origin.
a. Write expressions for the x- and y-components of the electric field at the origin due to a small piece of charge at angle u.
b. Write, but do not evaluate, definite integrals for the x- and y-components of the net electric field at the origin.
c. Evaluate the integrals and write E u net in component form
Step By Step Solution
Step 1 of 5
Consider a plastic rod bent into a quarter circle:
The linear charge density of the plastic rod is:
Now assume that the plastic rod is made up of small differential elements of arc length
Therefore;
The charge on each differential element is: