Continuous Charge Distributions

Transcription

1 Continuous Chge Distibutions Review Wht if we hve distibution of chge? ˆ Q chge of distibution. Q dq element of chge. d contibution to due to dq. Cn wite dq = ρ dv; ρ is the chge density. = 1 4πε 0 qi 1 dq ˆ i ˆ = 2 2 4πε i i 0 V dq 1 4πε 0 V dv P d ρdv 2 ˆ 1. Cn use clculus to detemine electic fields fo few specil chge distibutions. 2. Method impotnt. Know how to do. 3. Fo most poblems, we cnnot solve them nlyticlly, but we cn solve using compute methods.

2 Wys to Visulize the Field Conside the field of positive point chge t the oigin vecto mp field lines chg chg Intoduced by Michel Fdy ( ) 8/29/2011 BACH2006

3 Rules fo Vecto Mps chg Diection of ows indictes the diection of the field t ech point in spce Length of ows is popotionl to the mgnitude of the field t ech point in spce 8/29/2011 BACH2006

4 Rules fo Field Lines gphicl tick fo visulizing fields Lines leve () chges nd etun to () chges Numbe of lines leving/enteing chge mount of chge Field lines neve coss Tngent of line = diection of t ech point Locl density of field lines ~ mgnitude of t ech point Applets:

5 xecise: UI2PF2: 6) A negtive chge is plced in egion of electic field s shown in the pictue. Which wy does it move? ) up c) left e) it doesn't move b) down d) ight 8/29/2011 BACH2006

6 xecise: UI2A3 Conside dipole (2 septed equl nd opposite chges) with the yxis s shown. Which of the following sttements bout x (2,) is tue? y Q 2 x Q () x (2,) < 0 (b) x (2,) = 0 (c) x (2,) > 0 8/29/2011 BACH2006

7 xecise: UI2A3 Conside dipole (2 septed equl nd opposite chges) with the yxis s shown. Which of the following sttements bout x (2,) is tue? y Q 2 x Q () x (2,) < 0 (b) x (2,) = 0 (c) x (2,) > 0 x Solution: Dw some field lines ccoding to ou ules. 8/29/2011 BACH2006

8 q q y θ The lectic Dipole x Wht is the field geneted by this ngement of chges? Clculte fo point long xxis: (x, 0) x =?? Symmety x (x,0) = 0 8/29/2011 BACH2006 y y =?? 1 q,0 2 sinθ 4πε ( x ) = 2 sin θ = y ( x ) 1,0 = 2 4 πε = x 0 q 2 ( 2 2 x ) 3/2

9 lectic Dipole Field Lines Lines leve positive chge nd etun to negtive chge Field lgest in spce between two chges We deived: 1 y ( x,0) = 2 4 πε... fo >>, y 0 ( 2 2 x ) 3/2 ( x,0) q 1 x 3 8/29/2011 BACH2006

10 Field Lines Fom Two Like Chges Thee is zeo hlfwy between the two chges >> : looks like the field of point chge (2q) t oigin 8/29/2011 BACH2006

11 xecise UI3A1 xmine the electic field lines poduced by the chges in this figue. Which sttement is tue? q 1 q 2 () q 1 nd q 2 hve the sme sign (b) q 1 nd q 2 hve the opposite signs nd q 1 > q 2 (c) q 1 nd q 2 hve the opposite signs nd q 1 < q 2

12 xecise UI3A1 xmine the electic field lines poduced by the chges in this figue. Which sttement is tue? q 1 q 2 () q 1 nd q 2 hve the sme sign (b) q 1 nd q 2 hve the opposite signs nd q 1 > q 2 (c) q 1 nd q 2 hve the opposite signs nd q 1 < q 2 Field lines stt fom q 2 nd teminte on q 1. This mens q 2 is positive; q 1 is negtive; so, not () Now, which one is bigge? Notice long line of symmety between the two, tht the field still hs positive y component. If they wee equl, it would be zeo; This indictes tht q 2 is gete thn q 1

13 lectic Dipoles Molecules cn hve pemnent dipole moment. Clled pol molecules. exmple: H 2 O Dipole moment: p = qd q d P q idel dipole Wht hppens to dipole in unifom electic field? q d P q

14 lectic Dipoles Molecules cn hve pemnent dipole moment. Clled pol molecules. exmple: H 2 O Dipole moment: p = qd q d P q idel dipole Wht hppens to dipole in unifom electic field? F d q P cn wite s: q θ τ = p F No net foce; but toque. toque = Fd sin θ = qd sin θ = p sin θ Coss poduct

15 lectic Dipoles A dipole in nonunifom electic field will expeience foce. Micowve ovens: dipole moment of wte used to cook food. Micowve fequency t ntul fequency of vibtion of wte. Molecules esonte with the pidly oscillting electic field nd bsob lge mount of enegy. The K of the excited molecules is conveted to theml enegy by collisions of the molecules. Non pol molecules: no pemnent dipole moment, but n electic field cn cuse n induced dipole moment by cusing chge seption. Molecules e polized.