Electric field at the origin due to a bent rod with uniformly distributed charge

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? y x a

2. 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? y dq   x a dE

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? y d ds  x a dE

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? y dq   x a dE

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?

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

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

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. You could start with Coulomb’s Law, re-write it to calculate the dF on q1=-qdue to dq2 (an infinitesimal piece of the rod), and then integrate over dq2. In other words, do the whole problem all over again. y -q x Or you could multiply the two slides back by –q, simplify if appropriate, and be done with it. a