Review for Midterm-1

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Oscar Dalton
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1 Review fo Midtem-1

2 Midtem-1! Wednesday Sept. 24th at 6pm Section 1 (the 4:10pm class) exam in BCC N130 (Business College) Section 2 (the 6:00pm class) exam in NR 158 (Natual Resouces) Allowed one sheet of notes (both sides) and calculato Need photo ID Send Pof. Tollefson if you need to take the make-up exam and explain why (tollefson@pa.msu.edu( tollefson@pa.msu.edu) Make-up exam is at 8am Thusday (meet at 3234 BPS by 7:55am) Use the help-oom to pepae Review in class on Tuesday

3 Electic Foce! The magnitude of the electostatic foce, F,, between 2 chaged paticles with chages 1 and 2, espectively, and sepaated by a distance is defined as F k k 1 4 πε N m 2 / C 2! This is Coulomb s law whee k is a constant! The foces on 2 point chages ae eual and opposite, pointing to (away fom) the othe paticle fo unlike (like) chages

4 Electic Field! Electic field, E,, is the foce pe unit positive test chage E F 0! Fo a point chage F k 0 2 so E k 2

5 Electic Field! E points towads a negative point chage and away fom a positive point chage.! Supeposition pinciple F E F + F E + E F n E n! Given the E field we can find the foce on chage F E

6 If the vecto addition gives zeo you do not need to calculate each one. Fo example, in the figue below, if 1 2 then E 1 + E 2 0 at the oigin and the field comes only fom 3.

7 Flux! Calculate flux of unifom E though cylinde Φ E da! 3 sufaces - a, b, and c Φ E da + E da + E da a b c

8 Flux E da E da cosθ

9 Gauss Law! Gauss Law ε 0 Φ enc! Also wite it as ε 0 E da enc! Net chage enc is sum of all enclosed chages and may be +, -,, o zeo

10 Example fo Gauss Law! Chage 1 inside! E0 inside conducto! Thus Φ0 fo Gaussian suface (ed line)! So net chage enclosed must be 0! Induced chage of 2-1 lies on inne wall of sphee! Shell is neutal so chage of 3-2 on oute wall

11 Chage distibutions! E field fom a continuous line o egion of chage! Use calculus and a chage density instead of total chage, Q! Linea chage density λ Q / Length! Suface chage density σ Q / Aea! Volume chage density ρ Q /Volume

12 Gauss Law (Fig )! Non-conducting sheet of chage σ ε 0 E da enc ε EA + EA) 0 ( σ A E σ 2ε 0

13 Electic Potential! Electic potential enegy U fo a constant E and wok done by the field U U f U i W U Fd Ed! Electic potential fo a constant E V U Ed

14 Electic Potential (Fig. 25-5) 5)! Wok done by field W! Used to find V 0 f i V f E ds V i E! Potential deceases if path is in the diection of the electic field W 0 f i ds

15 Quiz - FGIIGG 1) Suppose we geneate an electic field of E What is the change in the electic potential, measued in Volts, associated with a moving a chage of 1.4 C fom (0,0) m to (2,2) m? V f E i ( V / m) ds! A) -400, B) -280, C) 600, D) -800, E) 1000 iˆ

16 Quiz - FGIIGG 2) Suppose we geneate an electic field of E 1.0 ( V / m) iˆ ( V / m) ˆj What is the wok done (in J ) by an extenal agent (W*) to move a chage of 6.0 C fom (0,0) m to (2,2) m? W* W f E ds! A) -6, B) 6, C) -36, D) 70, E) i

17 Electic Potential Summay fo a point change F k E k V k

18 Electic Potential (Fig. 25-3)! Dashed lines ae the edge of euipotential sufaces whee all points ae at the same potential.! Euipotential sufaces ae always to electic field lines and to E.! In this example V deceases by constant intevals fom the positive chage to the negative chage

19 Electic Potential! Use supeposition pinciple to find the potential due to n point chages V n i 1 V i k n i 1 i i! This is an algebaic sum, not a vecto sum! Include the sign of the chage

20 Electic Potential (Mathematica( Mathematica) -50 V5V0 0 V V50

21 Electic Field fom Potential! Take s axis to be x, y,, o z axes E x V V, Ey, x y E z V z! If E is unifom and s is to euipotential suface E V s

22 Potential Enegy! Total potential enegy fo a collection of chages is the scala sum of individual potential enegies - wok euied to assemble the chages U U + U U + U U + U U12 k d! whee etc

23 Capacitance! Calculate C of a capacito fom its geomety using steps:! 1) Assume chage,,, on the capacito! 2) Find E between using and Gauss law ε 0! 3) Find V fom E using! 4) Get C using C E da enc V V f E i d s

24 Capacitance (Fig. 26-5)! Paallel-plate capacito C ε d A 0 4 π A k d! Only depends on aea A of plates and sepaation d! C inceases if we incease A o decease d

25 Enegy in a Capacito! Wok euied fom 0 to total chage is W 1 C 0 d 2 2C! Potential enegy wok U 2 2C! O, use CV U 1 CV 2 2

26 Capacitance! Capacitos in paallel! V acoss each is eual! Total is sum! Capacitos in seies! is eual on each! Total V is sum n C C e i i n 1 1 C C e i i

27 Capacitance! Place a dielectic in capacito its capacitance inceases by numeical facto.! Called dielectic constant, κ C κ dielectic C ai

ELECTROSTATICS::BHSEC MCQ 1. A. B. C. D.

ELECTROSTATICS::BHSEC MCQ 1. A. B. C. D. ELETROSTATIS::BHSE 9-4 MQ. A moving electic chage poduces A. electic field only. B. magnetic field only.. both electic field and magnetic field. D. neithe of these two fields.. both electic field and magnetic