PHY132 Lecture 6 02/05/2010. Lecture 6 1
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1 Claical Phyic II PHY3 Lectue 6 The lectic Potential ti - II /5/ Lectue 6
2 Wok by a Vaying Foce Wok i a cala quantity, an we can thu a little piece of wok togethe, i.e. um a eie of ot-pouct of the foce F( i) with mall pat i of the total tajectoy F j F i θ j θ i θ k /5/ Thu, the geneal efinition of Wok: W lim F F( ) ie i.e. fo F() contant: n i i = n i = ( ) W= F () = F = F = F Δ = FΔcoθ Lectue 6 F k F,
3 /5/ (lectic) Potential negy an Potential When the lectic foce oe net wok W F l (eithe poitive o negative) on a chage, the eult i a change in it kinetic enegy: F net = ma W net F net l =ΔK =Δ(½mv ) The electic foce i a conevative foce, o we may aociate an LCTRIC POTNTIAL NRGY with the foce (a fo ANY conevative foce!): W = ΔU: ΔU = U f U i = W,i f i f F l A we i fo the electic fiel, we can now make the enegy INDPNDNT of the value of the chage by efining a POTNTIAL V() a the Potential-negy-pe- unit--chage: f f ΔU i f Δ V V( ) ( ) i = f f V i = = q q F i i Lectue 6 3
4 If the electic fiel i zeo eveywhee, the potential A. i zeo eveywhee B. i contant an the ame eveywhee C. vaie a you go along /5/ Lectue 6 4
5 Potential negy fo a Point Chage Conie a point chage : the Wok on chage q, by electic foce F moving q fom to i then: q q θ /5/ q coθ W = = ( ) = = F 4 U() q q = U U U = Δ = U ( ) = q q (, ) πε ( ) q ( ) V = fo Point Chage; o outie a Spheically Symmetic chage Note, with thi choice: U (= ) =, V (= ) = U q an again: F = = V = = Lectue 6 5
6 The Potential of a Point Chage The POTNTIAL i the Potential ti negy ivie i by q the chage : V ( ) U ( ) fo a point chage, o fo a = = q pheically ymmetic chage Fo ANY geneal lectic Fiel: ΔV a b = V b V a = a b eg e.g. fo contant: = (σ/ε )i: ΔV = = (σ/ε ) ( b a ) Conequence & Note: Potential V i a SCALAR (NON-vecto) quantity! The zeo-point of V i abitay: what ht count i the DIFFRNC ΔV! Check the ign of ΔV uing common ene! The fiel i minu the GRADINT of V: = V/, y = V/y, z = V/z INSID a conucto the POTNTIAL IS CONSTANT (becaue =!) Unit fo potential: VOLTS = V = J/C = Nm/C /5/ Lectue 6 6
7 Fo a unifom fiel = i,, the potential A. i contant too B. inceae with C. eceae with /5/ Lectue 6 7
8 Paallel Plate Two lage paallel l plate with unifom chage enitie +σ an σ, epaate by itance. i plate : σ σ Fiel ( ) = n = (in between the plane; zeo outie!) ε ε Potential Diff.: ΔV ( ) = V () V ( ) = W ( ) q = W( ) q /5/ V=σ/ε +σ σ O V() () Note: the potential V gow going upteam to the fiel σ/ε = F q = σ σ σ = q q = = ε ε ε V= [ ] σ V () = ε ( ) plane of chage + choice: V ( = ) = ( ) choice: ( ) = Δ V = V( = ) V( = ) = σ σ Note: = V = ( ) =+ ε ε σ an between the plate Lectue 6 8 σ
9 Two Coaial Cyline Single cyline aiu R, chage enity λ: λ ( ) = (pointing out!) Aume > >R; πε thu we epect ΔV> λ ΔV( ) = V( ) V( ) = W( ) q = W( ) q λ λ λ = = = = ln > > πε πε πε λ R λ R λ R = ln ln V () = ln πε πε πε Two long coaial conucting cyline, aii a an b>a, with linea chage enitie +λ (inne) an λ (oute cyline) : + λ+ ( λ) long unifom cyline; > R b: ( ) = =, ( V( ) = contant) πε b +λ = bin bin λ λ λ a < b : in ( ), = = = πε V () ln πε πε πε b : ( ), ( ) ln in λ b in < a = V = Note: V ln πε a πε /5/ () ( if ) thu V( )! an V(=R)= λ () λ b in +λ between Lectue 6 the cyl' 9 b in = = =+ πε a λ
10 Chage Sphee Single conucting phee aiu R an chage : ( ) = ( fo R, ele = ; ( = ) =! aume: > ) ΔV( ) = V ( ) V ( ) = W( ) q = W( ) q move //, q i.e. out- = k q = k = k k = wa! V ( R) = k ; V ( < R) = k R V ( ) = k Two concentic conucting phee with ih R, an R >R, : + k( + ) k( + ) R : ( ) = k : V( ) = V( R ) = R V() k R < R : () = : Δ V() = V() V( R ) = k < R R < R : ( ) =, Δ V ( ) = V ( ) = V ( R ) /5/ < R Note: = V = V( ) V( R ) = k =+ R between contant R Lectue 6 R the ph'
11 The value of the potential at a cetain point A. eally oen t matte; it i the potential iffeence between two poition that oe matte B., if the point i at infinity, i alway zeo C. oe matte, an i a funamental quantity /5/ Lectue 6
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