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Electrostatics: charges and fields One technique uses tiny spheres (about 10−4 m in diameter) that are black on one side and white on the other, with the sides being oppositely charged. Another technique uses similarly tiny spheres that are filled with many even tinier charged white particles along with a dark dye. In both cases, a narrow gap between sheets of electrodes (with one sheet being the transparent sheet that you look through) is filled with the spheres. By depositing a specific pattern of charge on the sheets, the color of the objects facing your eye can be controlled. In the first system, the black and white spheres rotate accordingly. In the second system, the tiny white particles pile up on one side of the sphere. In contrast with a standard LCD computer screen, electronic paper acts like normal paper, in that it doesn’t produce its own light; an outside light source is needed to view the page. An important advantage of electronic paper is that it uses a very small amount of power. A battery is needed only when the page is refreshed, whereas an LCD screen requires continual refreshing.
CHAPTER SUMMARY • Electric charge, which can be positive or negative, is both conserved and quantized. The force between two charges is given by Coulomb’s law: F=
1 q1 q2 rˆ 21 . 2 4π 0 r21
(1.57)
Integrating this force, we find that the potential energy of a system of charges (the work necessary to bring them in from infinity) equals 1 1 qj qk . 2 4π 0 rjk N
U=
(1.58)
j=1 k =j
• The electric field due to a charge distribution is (depending on whether the distribution is continuous or discrete) 1 E= 4π 0
ρ(x , y , z )ˆr dx dy dz
r2
or
N 1 qj rˆ j . (1.59) 4π 0 r2 j=1 j
The force on a test charge q due to the field is F = qE. • The flux of an electric field through a surface S is = E · da.
(1.60)
S
Gauss’s law states that the flux of the electric field E through any closed surface equals 1/ 0 times the total charge enclosed by the