1. Added Notes
August 31, 2005

2. Definitions Electric Field = Force per unit charge.
Types of charge distributions
Point Charges
Lines of Charge
Areas of Charge
Volumes of Charge
General:

3. Point Charges
In the Figure, the four particles are fixed in place and have charges q1 = q2 = +5e, q3 = +3e, and q4 = -12e. Distance d = 9.0 mm. What is the magnitude of the net electric field at point P due to the particles?
                                              

4. Line of Charge
Need m =charge per unit length  r ds
dq=m ds

5. A Harder Problem setup q dEy dE r x A line of charge dx
m=charge/length

6. (standard integral)

7. Completing the Math
1/r dependence

8. Surface Charge
Need Surface Charge density = s =charge per unit area. r
runit dA 

9. Define surface charge density
The Geometry
Define surface charge density
s=charge/unit-area
dq=sdA
(z2+r2)1/2
dA=2prdr
dq=s x dA = 2psrdr

10. (z2+r2)1/2 q

11. Final Result
(z2+r2)1/2

12. Look at the “Field Lines”

13. Kinds of continuously distributed charges
Line of charge
m or sometimes l = the charge per unit length.
dq=mds (ds= differential of length along the line)
Area
s = charge per unit area
dq=sdA
dA = dxdy (rectangular coordinates)
dA= 2prdr for elemental ring of charge
Volume
r=charge per unit volume
dq=rdV
dV=dxdydz or 4pr2dr or some other expressions we will look at later.

14. dq=rdV=r x surface area x thickness
The Sphere r dq
thk=dr
dq=rdV=r x surface area x thickness
=r x 4pr2 x dr

15. Summary (Note: I left off the unit vectors in the last
equation set, but be aware that they should
be there.)

16. The figure shows two concentric rings, of radii R and R ' = 3
The figure shows two concentric rings, of radii R and R ' = 3.25R, that lie on the same plane. Point P lies on the central z axis, at distance D = 1.90R from the center of the rings. The smaller ring has uniformly distributed charge +Q. What must be the uniformly distributed charge on the larger ring if the net electric field at point P due to the two rings is to be zero? [-5.39]   Q

17. The figure shows a plastic ring of radius R = 46. 0 cm
The figure shows a plastic ring of radius R = 46.0 cm. Two small charged beads are on the ring: Bead 1 of charge µC is fixed in place at the left side; bead 2 of charge µC can be moved along the ring. The two beads produce a net electric field of magnitude E at the center of the ring. At what positive and negative values of angle   should bead 2 be positioned such that E =   105 N/C? (Measure the angle from the positive x axis taking counterclockwise to be positive.)

19. In the figure, a thin glass rod forms a semicircle of radius r = 4
In the figure, a thin glass rod forms a semicircle of radius r = 4.00 cm. Charge is uniformly distributed along the rod, with +q = 4.00 pC in the upper half and -q = pC in the lower half.
(a) What is the magnitude of the electric field at P, the center of the semicircle? [28.6] N/C (b) What is its direction? [-90]° (counterclockwise from the positive x axis)

21. ds dq q