List of Necessary and Unnecessary EquationsPhysics 260FINAL EXAMMWF 10:10-11:00 Dr. WombleName:_______________________________Instructions: Work ONLY 10 of the 12 problems. Cross-out the problems that you will not work. NO EXTRA Credit will be given for working more than 10 problems. THE MORE WORK SHOWN, THE MORE CREDIT GIVEN!Constants:k=o41 = 9 x 109 Nm2/C2o = 8.85 x 10-12 C2/ Nm20 = 4 x 10-7 Tm/Amass electron, me = 9.11 x 10-31 kgelectron charge, e = -1.6 x 10-19 CConversions:1 eV =1.6 x 10-19 JUnits:V = J/C ; A= C/s ;  = V/A; F = C/V ; W = J/s ; T= N/(A*m) ; Wb = T*m2 ; H = T*m2/A 1) Maxwell’s Equations (2 pts each):a) Write the Maxwell equation which describes how a magnetic field lines do notdiverge from any point in space or converge on any point; that is it implies that isolated magnetic poles do not exist?b) Which Maxwell equation relates the electric field, E, to the rate of change of the magnetic field vector, B?c) In part b), does the electric field which is created by the changing magnetic field: converge, diverge, or is shaped similarly to a magnetic field? d) What is the Maxwell equation which describes how the magnetic field lines encircle an area through which current is passing or through which the electric flux is changing?e) What is the Maxwell equation which describes how electric field lines divergefrom positive charges and converge at negative charges?2) A proton moves in a circular orbit of radius 65 cm perpendicular to a uniform magnetic field of magnitude 0.75 T. Mass of proton=1.7 x 10-27 kg.a. What is the period of the motion?b. Find the speed of the proton.3) What is the electric field (magnitude and direction) in terms of k and charge, q, at Point P in the diagram below ?2qq1m1m1mPoint P4) Find the value of the integral B s-d for the surfaces depicted in the diagram below.A “x” denotes a current going into the page and a “o” denotes a current going out of the page. The value of the current is given in terms of “i" and is placed next to its respectivecurrent. Hint: Use only the Ampere portion of the Ampere-Maxwell Equation.a) Surface 1: XOXXOO2i3iiii2iSurface 1Surface 3 Surface 2b) Surface 2:c) Surface 3:5) An electron moves in a circular orbit about a stationary proton. The centripetal force is provided by the electrostatic force of attraction between the proton and electron. The electron has kinetic energy of 2.18 x 10-18 J.a. What is the speed of the electron? b. What is the radius of the orbit of the electron? (Hint: Centripetal force = rmv2 and KE=1/2 mv2 can be re-written as 2*KE = mv2)6) Two concentric spheres have radii 1.5 m, and 2.5 m. The inner sphere has a surface charge of -2q, and the outer sphere has a surface charge of 4q. Find in terms of k (=14 0) and q, the electric field at: 1.5 m2.5 m-2q4qHint: )4(2rEdaE=qenc/a) r = 1 mb) r = 2mc) r= 3 m 7) The electric potential in a region of space is given by the following function:yzxzyxV 52),,(2where 2 and 5 have appropriate units (i.e. don’t worry about them).Find the magnitude of the electric field at a point x=2 m, y= 1m, and z= 2 m.8) Find the currents through each of the resistors below: (Note: 8 pts will be given for theproper arrangement of the linear equations. Write down your equations in a clear form.)9) Find the currents through each of the resistors shown.5 V12 V4 2 3 0.2 2 2 3 46 V50 H100 pF1 M10) The power supply in the circuit below has a linear frequency of 100 Hz:a) What is the impedance of the circuit? (3pts)b) What is the phase angle? (3pts)c) What is the natural frequency of this circuit? (3pts)d) Does the current lead or lag the voltage? (1pt)11) A 6 V battery of negligible internal resistance is used to charge a 2 F capacitor through a 100  resistor. a. Find the initial currentb. Find the final charge on the capacitor.c. Find the time required for the charge to reach 90% of its final value.12) In the circuit below, the battery has a potential difference of 10V and the five capacitors each have a capacitance of 10 F. a. What is the charge on capacitor C1?b. What is the charge on capacitor C2?C1C210 VList of Necessary and Unnecessary Equations1. F = 22141rqqo2. F=qE3. E = rˆ412rqo4. E = qF5.0encqd aE6.encoq7. E=o8. E=o29. E = ro210. V = qW11. Vf - Vi = fidsE12. V= rqo4113. V=niiioniirqV114114. Es= -sV15. i =  AJ d16. R= iV17.JE118. R =AL19. P= iV = i2R = RV220. Fc = rmv221. K = ½ mv222. L = mvr23.T =vr224. f=T125. F = q v  B26. F = i L  B27. = N i A28. dB = 2ˆ4ridors 29. B =rio230. B =rio231. B= 0 i n32.encid0sB33. Fba= ibLBa34.B  dA 035.E s d -ddtB36.B s  dddti0 0E0 enc  37. E=dtd-B38. id =dtd E039. E = i R40. q = C V41. Ceq =  Cj (parallel)42. eqC1 = jjC1 series43. U = q2/ (2C)44. Req =  Rj (series)45. eqR1 = jjR1 (parallel)46. C = R*C47. q = C E (1 – exp (-t/(RC))) (charging)48. i = (E/R) *exp (-t/(RC)) (charging)49. q= qo*exp (-t/(RC)) (discharging)50. i = -(q0/(RC)) * exp (-t/(RC)) (discharging)51. L = (N)/i52. E = -Ldtdi53. U = ½ Li254.  = LC155. Z2 = R2 + (XL – XC)256. tan  = (XL – XC)/R57. XL = d * L58. XC = Cd159. Irms = Imax / 260. VS = Vp PsNN61.  = 2f62. c =