1. Chapter 23--Examples

2. Problem
In the figure below, point P is at the center of the rectangle. With V=0 at infinity, what is the net electric potential at P due to the six charged particles?
-2q
+3q
+5q
-3q P d

3. Find distance from corners to P
-2q
+3q
+5q
-3q P d s
d/2

4. Potentials (Voltage) is a scalar2 3 1
-2q
+3q
+5q
-3q P d s
d/2 4 5 6

6. Problem
A charge q is distributed uniformly throughout a spherical volume of radius, R.
Setting V=0 at infinity shown that the potential at a distance r from the center, where r<R is given by
What is the potential difference between a point on the surface and the sphere’s center?

7. First, use Gauss’s law to find the E-field inside and outside the sphere

8. Outside is simpler

9. Inside

10. Voltage=Outside+Inside

11. Part b) What is the potential difference between a point on the surface and the sphere’s center?

12. Okay, that is if V=0 at infinity what if V=0 at the center of the sphere?
Same as previous
Same as previous

13. Problem The electric potential at points in a space are given by
V=2x2-3y2+5z3
What is the magnitude and direction of the electric field at the point (3,2,-1)?

14. E=-grad(V)

15. Directions
Direction w.r.t +x axis
Direction w.r.t +z axis

16. Problem
Three C charges form an equilateral triangle, 1.7 m on a side. Using energy that is supplied at a rate of 0.83 kW, how many days would be required to move one of the charges to the midpoint of the line joining the other two charges?

17. Draw It Initially, this charge is 1.7 m from the other two charges
Finally, this charge is 0.85 m from the other two charges

18. Potential Difference

19. Potential Energy

20. Power=Work per unit time
P=W/Dt
W=-DU
So 0.83 kW= 830 J/s
And Dt= DU/P=152x106/830
Dt=183,699 s or 51 hours or 2.12 days