Lesson 2: Ch. 22 (1-3) – Electric Field 1 The Electric Field E 3 Superposing E fields. 4 Electric Dipoles.

Charged particles exert forces on each Several charges create a NET E that can An electric dipole is two equal magnitude other without touching (action at a dis- be sketched or vector added. The rules: electric charges (one positive, one nega- tance). How? We say that electric charge tive) held apart by some distance d. It • Electric field lines point directly to- creates electric fields around themselves generates an electric field that is simple wards “-” or away from “+”. that affects other charges. enough to work with as an example. • Every charge mades an E at every At each point in space you find the E is a vector field – a function where point – they add (superpose). direction of the electric field by adding each different location has an individual the electric field from each point charge value and direction for the electric field. • A charge’s E is stronger close by it. (E ,E ) to find the net electric field E. A wind-speed map is a vector field too 1 2 • Because the net E is a superposi- For one point in space the process looks (position, strength, direction). tions its field lines never cross. like this picture: • E line density proportional to 2 Electric Field Model strength. An isolated point charges is simple! For any single point charge q, the electric field is just Coulomb’s Law, removing the other charge q0 from the equation: Doing this at several points in space ~ F~ |q| lets you “fill in the gaps” to get the net E = q = k r2 rˆ 0 electric field. Units of E are N/C (Force/charge). More than one charge? Add vector Knowing E we get the force on any E’s at each point to find net field. charge q0 sitting anywhere easily:

F~0 = q0E~

Easier to find E for a group of parti- cles than to calculate F for each...

1 Exercise 1: In the figure, equal- Exercise 2: The figure shows a Exercise 3: The figure shows an magnitude charges ±q are distributed as charged particle and a point in space electric dipole with its dipole moment shown. Draw the electric field vectors at marked P . What are the x and y com- pointing in the −z direction, and P marks points A–E. ponents of the electric field at P ? a location on the x axis. The text shows how to use superposition to find the elec- B y (cm) tric field magnitude at points along the z axis (p. 636). What is the field magnitude A D P at points along the x axis?

C Key ideas: 45 nC • Superposition: add components to ~ E x (cm) get overall components of E. • Look for components that cancel by symmetry! z

−q d/2 P x d/2 +q

x

2