Added Notes August 31, 2005

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

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?                                               

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

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

(standard integral)

Completing the Math 1/r dependence

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

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

(z2+r2)1/2 q

Final Result (z2+r2)1/2

Look at the “Field Lines”

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.

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

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

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

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 +2.00 µC is fixed in place at the left side; bead 2 of charge +5.60 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 = 2.00   105 N/C? (Measure the angle from the positive x axis taking counterclockwise to be positive.)

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 = -4.00 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)

ds dq q