FINAL EXAMDecember 11, 1997Name:_________________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.Question 1)a) Find the net force (magnitude and direction) on the charge, q, at Point P in terms of k, charge, q, and distance, d. k =14 02qq-qqq-45013502dddddqPoint Pb) What is the magnitude and direction of the electric field at Point P?Question 2) What is the electric field (magnitude and direction) in terms of k and charge, q, at Point P in the diagram below ?2qq1m1m1mPoint PQuestion 3)Find the electric potential at point P in terms of k, charge, q, and distance, d, for the system of six point charges shown below. It is not necessary to algebraically simplify your answer.2qq-qqq-45013502dddddPoint PQuestion 4) 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-2q4qa) r = 1 mb) r = 2mc) r= 3 mQuestion 5) Find the currents through each of the resistors shown.Question 6) In the figure below, the battery has a potential difference of 20 V. Find (a) the equivalent capacitance of all the capacitors;(b) the charge stored on that equivalent capacitance. Give the potential across and the charge on (c) capacitor C1 and(d) capacitor C2.8F6F4FC1 = 6F8FC2 = F50 VQuestion 7) Find the current through each of the resistors.0.2 2 2 3 46 V4  2 3 12 V12 VQuestion 8) An alpha particle (2 protons and 2 neutrons, charge = 2e) travels in a circular path of radius 1 cm in a magnetic field with B= 1.0 T. Calculate:Data:m = 6.68 x 10-27 kgelectron charge = 1.6 x 10-19 CA) its speed:B) its frequency of revolution,f (not :C) its kinetic energy in electron volts (1 eV = 1.6 x 10-19 J)D) the potential difference through which it would have to be accelerated to achieve this energy.Question 9) If d=377 rad/s, R= 100 , C=15 F, Em = 36 V in circuit below. What is the impedance, Z, and the phase constant, , of the circuit?Question 10) 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 respective current. Hint: Use only the Ampere portion of the Ampere-Maxwell Equation.a) Surface 1: XOXXOO2i3iiii2iSurface 1Surface 3 Surface 2b) Surface 2:c) Surface 3:Question 11) a) What is the equivalent resistance of the network of resistors shown?b) What is the current through each resistor?36 V100 15 F100 50 75 50 6 VQuestion 12) In the figure, the long straight wire carries a current of 50 A and the rectangular loop carries a current of 20 A. a) Calculate the resultant force acting on the loop. Assume that a=1 cm, b = 1 cm and L=30 cm. 0= 1.3 x 10-6 T*m/Ab) Is the loop being pulled towards the long wire or pushed away from it?ab50 AL20 A20 AList of Necessary and Unnecessary Equations(Bold face indicates vector)F = (k q1 q2)/r2F=qvB F =mv2/r F=q1E F=i1 L B2E = (k q2 r)/r2E(4r2) = qenc/E = E= -V/SV= Vi = kqi/riV = i R V= q/c V = -L (di/dt)q = CV C = (0 A)/d U=q2/2C U= (CV2)/2i = dq/dt J = i/A i = V/RP= i2R = V2/RReq = R1 + R2 +…+ Rn (series)KE = (mV2)/2 PE =mgh KE=charge*voltage = 2f T = (2r)/v f = 1/TB2= 0i2/(2d) B(2r) = 0iencL= (N/i L/l =0n2AU = (Li2)/2id= 0 (d/dt)E  d q /encA 0B  dA 0E s d -ddtBB s  dddti0 0E0 enc  Z =R + (X - X )2L C2tan  = (XL - XC) /RXL= d L XC = 1/(d