Exam 2PHY206110-21-04Name:_______________________ ___H-ITT or pseudonym: ______________Exam 2Closed book exam. A calculator is allowed, as is one 8.511” sheet of paper with your own written notes. Please show all work leading to your answer to receive full credit.Exam is worth 100 points, 25% of your total grade.UF Honor Code: “On my honor, I have neither given nor received unauthorized aid in doing this exam.”Page 1 of 10Sphere: 2 244 3.14159273S r V rp p p= = =319.11 10 kgem-= �9 2 2019 10 N m / C4Kpe= = � 12 2 208.8542 10 C / N me-= � e 16022 1019. C1 2122ˆq qKr=F renc0SqdeF = � =�Ε Α�0re�� =EV=- �E0UVq=0q=FECW U d=- D = ��F sCV dD =- ��E s( )ˆ ˆˆx y zx y zgrad f f� � ��= + +� � �= =�F( )yxzFFFdivx y z����� = = + +� � �F F V SdV d�� = �� �F FΑ� Q C V= D( )2212 2QU C VC= D =eff 1 2C C C= +eff 1 21 1 1C C C= +V iRD =22 VP Vi i RR= = =eff 1 2R R R= +eff 1 21 1 1R R R= +LRAr=dqidt=c 3 0 108. m/s1 eV J 16022 1019.112 2v c/t t 0LL0( )( )2/x x vtt t vx cgg�= ��= �y yz z21xxxu vuvuc��=�21yyxuuvucg�=� ��� �� �E mc2( )21K mcg= -p umF pd dt/m c E p c2 4 2 2 2 F E v B q( ) i=F L × B0wire2ˆ ˆ2ikir rmp= =B r r70210 T m / A4Kkcmp-= = = �604 1.257 10 T m /Akm p-= = � �PHY206110-21-04Name:_______________________ ___H-ITT or pseudonym: ______________1. Consider the circuit above. The battery supplies an EMF of = 6.0 V, and the resistances of the 3 resistors are1100R = W, 225R = W, and 375R = W(a) [6 points] Find the voltage drop between points a and b: ab a bV V VD = -.(b) [6 points] Find the current through resistor R2. Page 2 of 10abR1R2R3+PHY206110-21-04Name:_______________________ ___H-ITT or pseudonym: ______________(c) [6 points] Find the total power dissipated in the circuit that must be provided by the battery.(d) [8 points] Suppose an identical circuit (with the same resistors and battery configuration) is connected to the above circuit at points a and b. That is, a conductor connects point a of the first circuit to point a of the second circuit, and another conductor connects point b of the first circuit to point b of the second. Calculate the voltage drop between points a and b for this combined circuit. (Hint: apply Kirchoff’slaws to each loop of the circuit.)Page 3 of 10PHY206110-21-04Name:_______________________ ___H-ITT or pseudonym: ______________3. Consider the circuit above. A battery supplies an EMF of = 12.0 V, the resistance11.25 MR = W, and the capacitors have capacitance 118 FC m= and 19 FC m=. Consider that switch S is closed at time t = 0. (61 M 10W= W, -61 F = 10 Fm).(a) [6 points] What is the time constant of the circuit that governs how fast the current changes after the switch is closed ?(b) [6 points] What is the maximum charge attained on the top plate of capacitor C1 (i.e. at point a) after the switch is closed?Page 4 of 10aR1C2C1+bSPHY206110-21-04Name:_______________________ ___H-ITT or pseudonym: ______________(c) [6 points] Sketch the voltage drop ab a bV V VD = - across the capacitors as a function of time t. Try to be accurate in your sketch.Page 5 of 10PHY206110-21-04Name:_______________________ ___H-ITT or pseudonym: ______________3. A new type of cannon can launch 5 kg projectiles at the high velocity of 0.3c(a) [6 points] What is the minimum amount of energy required to accelerate a projectile from rest to this final velocity?(b) [6 points] If the cannon is mounted on the front of a spaceship traveling away from Earth at a velocity of 0.6c, what will be the velocity of the launched projectile in the reference frame of the Earth?Page 6 of 10PHY206110-21-04Name:_______________________ ___H-ITT or pseudonym: ______________4. A kaon is an unstable particle with a rest mass energy of 500 MeV and an average lifetime of 85.2 10 st-= � in its rest frame. Consider a beam of kaons, where each kaon has a momentum of 1000 MeV/c as measured in a laboratory. (1 MeV = 131.6 10 J-�)(a) [6 points] What is the velocity of each kaon in the laboratory?(b) [6 points] What is the average distance the kaons travel at this momentum in the laboratory before decaying?Page 7 of 10PHY206110-21-04Name:_______________________ ___H-ITT or pseudonym: ______________5. A long straight wire has an electric charge density of 7.0 / mCl m= along its length, where 61 10C Cm-=, as measured in the rest frame of the wire. (a) [6 points] What is the observed charge density of the wire as measured by an observer traveling at a velocity of 82.4 10 m/sv = � parallel to the direction of the wire?(b) [6 points] What is the observed charge density of the wire as measured by an observer traveling at a velocity of 82.4 10 m/sv = � perpendicular to the direction of the wire?Page 8 of 10PHY206110-21-04Name:_______________________ ___H-ITT or pseudonym: ______________6. [8 points] A beam of electrons (“cathode rays”) is sent between two parallel electric plates separated by a distance d = 1.5 cm with a potential difference of 300 V between them. The electric field points in the ˆ+y direction. If the electron beam travels perpendicular to the electric field in the ˆ+x direction, and each electron has a kinetic energy of 5,000 eV, what magnetic field is necessary (direction and magnitude) so that the electrons continue traveling in a straight line without deflection by the electric field? The charge of the electron is191.6 10 Cq e-=- =- �, the electron rest-mass energy is 511,000 eV, and 191 eV = 1.6 10 J-�.Page 9 of 10 + + + + + + + e-xyEdPHY206110-21-04Name:_______________________ ___H-ITT or pseudonym: ______________7. Consider two parallel wires, A and B, separated by a distance d = 0.5 cm as shown above. The current of wire A is 9 AAi =, and the current of wire B is 3 ABi =, both in the ˆxdirection.(a) [6 points] Calculate the direction and magnitude of the magnetic field at point C, midway between the two wires in the plane of the wires.(b) [6 points] Find the direction and magnitude of the force per unit length (per meter) on wire B arising from the interaction of its current with the magnetic field of wire A.Page 10 of 10di Ai
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