Review fo Midtem-1
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 email 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
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 1 2 2 k 1 4 πε 0 8.99 10 9 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
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
Electic Field! E points towads a negative point chage and away fom a positive point chage.! Supeposition pinciple F E F + F +... + 1 2 E + E +... + 1 2 F n E n! Given the E field we can find the foce on chage F E
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.
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
Flux E da E da cosθ
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
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
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
Gauss Law (Fig. 24-15)! Non-conducting sheet of chage σ ε 0 E da enc ε EA + EA) 0 ( σ A E σ 2ε 0
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
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
Quiz - FGIIGG 1) Suppose we geneate an electic field of E 200.0 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
Quiz - FGIIGG 2) Suppose we geneate an electic field of E 1.0 ( V / m) iˆ + 2.0 ( 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) -24 0 i
Electic Potential Summay fo a point change F k E k 2 2 0 V k
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
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
Electic Potential (Mathematica( Mathematica) -50 V5V0 0 V50 +50 V50
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
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 12 23 + U + U 13 24 + U + U 14 34 11 12 13 14 12 U12 k d! whee etc
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
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
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
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
Capacitance! Place a dielectic in capacito its capacitance inceases by numeical facto.! Called dielectic constant, κ C κ dielectic C ai