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 (₂ P (a) Find the angle in radians, 0, subtended by the arc and the linear charge density 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) ind he 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 (₂ P (a) Find the angle in radians, 0, subtended by the arc and the linear charge density 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) ind he 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
Chapter6: Gauss's Law
Section: Chapter Questions
Problem 45P: Repeat your calculations for the preceding problem, given that the charge is distributed uniformly...
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