329lect02 (1) - 2 Static electric fields — Coulomb’s...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 2 Static electric fields — Coulomb’s and Gauss’s laws Static electric fields are produced by static (i.e., non-time varying) distribu- tion of charges in space. At the most elementary level, each stationary point charge (electron or proton) Q is surrounded by its radially directed electrostatic field E given by Coulomb’s law , and in the presence of multiple charges the field vectors of all the charges are added vectorially (linear superposition holds) to obtain the superposition field E . • Coulomb’s law specifies the electric field of a stationary charge Q at the origin as E ( r ) = Q 4 π o r 2 ˆ r as a function of position vector r = ( x, y, z ) , where o ≈ 1 36 π × 10 9 F/m is a scaling constant known as permittivity of free space , r = | r | = x 2 + y 2 + z 2 is radial distance from the charge, and ˆ r = r r radial unit vector pointing away from the charge. r = | r | ˆ r Q q ˆ r Force exerted by Q on q: F = q E E = Q 4 π o | r | 2 ˆ r with electric field With multiple Q’s superpose multiple E’s x y z – This Coulomb field E ( r ) will exert a force F = q E ( r ) on any stationary “test charge” q brought within distance r of Q (see figure in the margin). 1 ◦ If qQ > , force F is repulsive (directed along ˆ r ), if qQ < it is attractive — like charges repel, unlike charges attract. – The existence of a Coulomb field accompanying each charge carrier in its rest frame 1 is taken to be a fundamental property of charge carriers (established by measurements). • When multiple static charges Q n are present in a region, the force on a stationary test charge q can be described as q E in terms of a superposition field E = n Q n 4 π o r 2 n ˆ r n written in terms of the magnitudes and directions of vectors r n pointing from each Q n to q . – Equivalently, we can write q x y z r- r n Q n r n r Position vectors of charges are referenced with respect to a common origin O O E ( r ) = n Q n 4 π o | r- r n | 2 r- r n | r- r n | , where r and r n now denote the locations of q and Q n with re- spect to a common origin — this form is more convenient when static electric field E is to be calculated for an arbitrary location r (independent of the test charge notion)....
View Full Document

{[ snackBarMessage ]}

Page1 / 8

329lect02 (1) - 2 Static electric fields — Coulomb’s...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online