1. A rod is bent into an eighth of a circle of radius a, as shown. The rod carries a total positive charge +Q uniformly distributed over its length. What is the electric field at the origin? a y x

2. a y x dE dq  

3. A rod is bent into an eighth of a circle of radius a, as shown. The rod carries a total positive charge +Q uniformly distributed over its length. What is the electric field at the origin? a y x dE ds  dd

4. A rod is bent into an eighth of a circle of radius a, as shown. The rod carries a total positive charge +Q uniformly distributed over its length. What is the electric field at the origin? a y x dE dq  

5. A rod is bent into an eighth of a circle of radius a, as shown. The rod carries a total positive charge +Q uniformly distributed over its length. What is the electric field at the origin?

7. You should provide reasonably simplified answers on exams, but remember, each algebra step is a chance to make a mistake.

8. a y x What would you do differently if we placed a second eighth of a circle in the fourth quadrant, as shown? What would be different if the charge were negative?

9. A rod is bent into an eighth of a circle of radius a, as shown. The rod carries a total positive charge +Q uniformly distributed over its length. A negative point charge -q is placed at the origin. What is the electric force on the point charge? Express your answer in unit vector notation. a y x You could start with Coulomb’s Law, re- write it to calculate the dF on q 1 =-q due to dq 2 (an infinitesimal piece of the rod), and then integrate over dq 2. In other words, do the whole problem all over again. Or you could multiply the two slides back by –q, simplify if appropriate, and be done with it. -q