Physics 2102 Lecture: 07 TUE 09 FEB

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1 Physics 2102 Jonathan Dowling Physics 2102 Lectue: 07 TUE 09 FEB Electic Potential II

2 PHYS2102 FIRST MIDTERM EXAM 6 7PM THU 11 FEB 2009 Dowling s Sec. 4 in??? YOU MUST BRING YOUR STUDENT ID YOU MUST WRITE UNITS TO GET FULL CREDIT The exam will cove chaptes 21 though 24, as coveed in homewok sets 1, 2, and 3. The fomula sheet fo the exam can be found hee: KNOW SI PREFIXES n, cm, k, etc.

3 Consevative Foces, Wok, and Potential Enegy W = F ( ) d Wok Done (W) is Integal of Foce (F) U = W F ( ) = du d Potential Enegy (U) is Negative of Wok Done Hence Foce is Negative Deivative of Potential Enegy

4 Coulomb s Law fo Point Chage F 12 = kq 1 q 2 2 Foce [N] = Newton E = kq Electic Field [N/C]=[V/m] U 12 = kq 1 q 2 Potential Enegy [J]=Joule V 12 = kq 2 Electic Potential [J/C]=[V] =Volt F 12 = du 12 E 12 = dv 12 d d q 2 q q 1 2 P P P P 1 U 12 = " F 12 d V 12 = " E 12 d

5 Continuous Chage Distibutions Divide the chage distibution into diffeential elements Wite down an expession fo potential fom a typical element teat as point chage Integate Simple example: cicula od of adius, total chage Q; find V at cente. dq V = = k dv = dq = k Q kdq Units : # Nm2 " C 2 C$ & = Nm m% " # C $ % & = J $ " # C% & ' V [ ]

6 Potential of Continuous Chage Distibution: Line of Chage Unifomly chaged od Total chage Q Length L What is V at position P? V = Q / L dq = dx = = " kdq L k# dx = ( L + a " 0 x) [ ln( L + a x ] L k ) 0 x dx L a P V = k ' ln & L + $% a a # " Units: [Nm 2 /C 2 ][C/m]=[Nm/C]=[J/C]=[V]

couse V = " E # ds f i Focus only on a simple case: electic field that points along +x

7 Electic Field & Potential: A Simple Relationship Notice the following: Point chage: E = kq/ 2 V = kq/ Dipole (fa away): E = kp/ 3 V = kp/ 2 E is given by a DERIVATIVE of V Of couse V = " E # ds f i Focus only on a simple case: electic field that points along +x axis but whose magnitude vaies with x. E x = dv dx Note: MINUS sign Units fo E: VOLTS/METER (V/m)

8 Unifomly chaged od Total chage Q Length L We Found V at P Find E fom V? x dx L E fom V: Example = Q / L a P " V = kln L + a % # $ a & ' { [ ] ( ln[ a] } = k ln L + a { [ ] ln[ a] } E = dv da = k" d da ln L + a # 1 = k" L + a 1 & $ ' % a( # = k" $ a L + a % ( L + a)a ( ) & ' ( = k" # L & $ ' % ( L + a)a( Units: Nm 2 # " C 2 C m m $ & = N $ % " # C% & = V $ " # m% & m 2 Electic Field

9 Electic Field & Potential: Question Hollow metal sphee of adius R has a chage +q Which of the following is the electic potential V as a function of distance fom cente of sphee? +q V (a) 1 V (b) 1 =R =R V (c) 1 =R

10 Electic Field & Potential: Example +q Outside the sphee: Replace by point chage Inside the sphee: E = 0 (Gauss Law) E = dv/d = 0 IFF V=constant E V dv E = d d " Q # = k d $ % & ' Q = k 2

11 Equipotentials and Conductos Conducting sufaces ae EQUIPOTENTIALs At suface of conducto, E is nomal (pependicula) to suface Hence, no wok needed to move a chage fom one point on a conducto suface to anothe Equipotentials ae nomal to E, so they follow the shape of the conducto nea the suface. V E

12 Conductos Change the Field Aound Them An Unchaged Conducto: A Unifom Electic Field: An Unchaged Conducto in the Initially Unifom Electic Field:

Shap Conductos Chage density is highe at conducto sufaces that have small adius of cuvatue E = σ/ε 0 fo a conducto, hence STRONGER electic fields at shaply cuved sufaces Used fo attacting o getting

13 Shap Conductos Chage density is highe at conducto sufaces that have small adius of cuvatue E = σ/ε 0 fo a conducto, hence STRONGER electic fields at shaply cuved sufaces Used fo attacting o getting id of chage: lightning ods Van de Gaaf -- metal bush tansfes chage fom ubbe belt Mas pathfinde mission -- tungsten points used to get id of accumulated chage on ove (electic beakdown on Mas occus at ~100 V/m) (NASA)

14 Ben Fanklin Invents the Lightning Rod

Squat low to the gound on the balls of you feet, with you feet close togethe.

15 LIGHTNING SAFE CROUCH If caught out of doos duing an appoaching stom and you skin tingles o hai ties to stand on end, immediately do the "LIGHTNING SAFE CROUCH. Squat low to the gound on the balls of you feet, with you feet close togethe. Place you hands on you knees, with you head between them. Be the smallest taget possible, and minimize you contact with the gound.

16 Summay: Electic potential: wok needed to bing +1C fom infinity; units = V = Volt Electic potential uniquely defined fo evey point in space -- independent of path Electic potential is a scala -- add contibutions fom individual point chages We calculated the electic potential poduced by a single chage: V = kq/, and by continuous chage distibutions : V = kdq/ Electic field and electic potential: E= -dv/dx Electic potential enegy: wok used to build the system, chage by chage. Use W = U = qv fo each chage. Conductos: the chages move to make thei suface equipotentials. Chage density and electic field ae highe on shap points of conductos.

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