A uniformly charged rod of length L is bent into an arc of radius R. Total charge on the rod is Q. This is the arc problem we considered in class. ( R P (a) Find the angle in radians, 0, subtended by the arc and the linear charge density λ in terms of Q, L and R. See the exercises and the hints and guide at the end of the homework for a reminder of the relationship between angle and arc length. (b) Find the field at a test point placed at the center of the circle that the arc is part of. Again, follow the process, and remember that the sample charge dq occupies a small length of the rod, and that length is now a small part of an arc. (c) Check that your results for the case L << R give you the field of a point source with charge Q, a distance R away. You will want to use the small angle approximation from the exercises: sin for 0 << 1
A uniformly charged rod of length L is bent into an arc of radius R. Total charge on the rod is Q. This is the arc problem we considered in class. ( R P (a) Find the angle in radians, 0, subtended by the arc and the linear charge density λ in terms of Q, L and R. See the exercises and the hints and guide at the end of the homework for a reminder of the relationship between angle and arc length. (b) Find the field at a test point placed at the center of the circle that the arc is part of. Again, follow the process, and remember that the sample charge dq occupies a small length of the rod, and that length is now a small part of an arc. (c) Check that your results for the case L << R give you the field of a point source with charge Q, a distance R away. You will want to use the small angle approximation from the exercises: sin for 0 << 1
Related questions
Question
Expert Solution
Step 1
Trending now
This is a popular solution!
Step by step
Solved in 5 steps with 4 images
Follow-up Questions
Read through expert solutions to related follow-up questions below.