Exam 3PHY206111-18-04Name:_______________________ ___Exam 3Closed 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. Answers should be calculated to 2 significant digits. 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 renc0ESqdeF = � =�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.F E v B q( ) i=F L ×B70210 T m / A4Kkcmp-= = = �604 1.257 10 T m /Akm p-= = � �3 i dd kr=s× rB0 enc Cd im� =�B s�0wire2ˆ ˆ2ikir rmp= =B r ri=μ A=τ r×F=τ μ× BU =- �μ Bzz zdBFdzm=BSdF = ��BΑBdNdteF=-LdiV LdtD =BNLiF=212U Li=22002 2EU BuVem= = +RCRCt =LRLRt =1LCLCw =SS PPNV VND = Dx x y y z za b a b a b�= + +a b( )( )( )y z y z x z x z x y x ya b b a a b b a a b b a� = - - - + -a b i j kPHY206111-18-04Name:_______________________ ___1. Consider the toroid shown with an inner radius a = 5 cm and an outer radius b = 6 cm. The total number of turns of wire wound around the toroid is N = 400. The core of the toroid has a rectangular cross-section with a thickness h = 0.5 cm. (a) [6 points] If the wire carries a current of 2A, what is the magnitude of the magnetic field inside the toroid at a radius midway between the inner and outer radii?Page 2 of 10PHY206111-18-04Name:_______________________ ___1. Continued(b) [8 points] Calculate the inductance of the toroid.2. [8 points] A long straight wire with a cylindrical cross-section has a radius of 0.3 mm and carries a current of 100 mA uniformly spread across its cross-section. What is the ratio of the magnetic field at a radius of 0.1 mm to that at the surface of the wire?Page 3 of 10PHY206111-18-04Name:_______________________ ___3. A square loop of wire with edge length 7 cm is located in the plane of the paper insidea homogeneous magnetic field of 0.35 T pointing into the paper. It is connected in series with a resistor of 210 . The magnetic field is now increased at a constant rate by a factor of 4.5 in 18 s. (a) [6 points] Calculate the magnitude of the induced EMF in the loop (in V) during that time.(b) [6 points] Calculate the current induced in the loop in Amps during that time.Page 4 of 10PHY206111-18-04Name:_______________________ ___4. A rectangular loop of wire is located in the plane of the paper inside a homogeneous magnetic field of 6 mT pointing into the paper. One side length is fixed at 50 cm, the other side grows with time according to the formula ( )01 at= +l l, where 050 cm=land -12.5 sa =.(a) [6 points] Calculate the magnitude of the induced EMF in the loop.(b) [6 points] If the resistance of the wire increases as ( )01R R tl= +, where03R = W and = 0.5 s-1, what would the acceleration of the moving wire needto be in order to maintain a constant current in the wire? Hint: Consider adding a quadratic time dependence to the length of the growing side.Page 5 of 10PHY206111-18-04Name:_______________________ ___5. A solenoid 42 cm long has a circular cross-section of 8.5 cm2. There are 420 turns of wire carrying a current of 3.25A. (a) [6 points] Find the magnitude of the magnetic field inside the solenoid assuming that it is essentially infinite in length (neglect end effects).(b) [6 points] Find the total energy stored in the magnetic field inside the volume of the solenoid. Neglect end effects.Page 6 of 10PHY206111-18-04Name:_______________________ ___6. An oscillating LC circuit consists of a 2 mH inductive coil and a 3 nF capacitor. The capacitor has a voltage drop of 2.8 V when the current through the coil is 1.2 mA. (a) [6 points] Find the period of oscillation.(b) [6 points] Find the maximum charge on the capacitor.(c) [6 points] Find the maximum current through the coil.Page 7 of 10PHY206111-18-04Name:_______________________ ___7. A frog can be considered a magnetic dipole when immersed in strong magnetic field (a property known as diamagnetism). (a) [3 points] Does the frog have greater potential energy when its magnetic dipole moment is aligned with the direction of the magnetic field or opposite to it? (b) [3 points] If the field is strong enough, it is possible to levitate the frog. Wouldthis occur near the center of a solenoid where the field is uniform, or near the end of a solenoid where the field is diverging?Page 8 of 10PHY206111-18-04Name:_______________________ ___8. Consider an RLC circuit connected to an alternating-current power supply. The power supply delivers an electric potential of ( )0sint te e w=.(a) [6 points] Write down a differential equation for the charge ( )q t on the capacitor.(b) [6 points] Estimate the current in the circuit for the following three limiting cases (give your reasons!): 1) 0w �, 2) w � �, and 3) 1LCw �Page 9 of 10(t)R CLPHY206111-18-04Name:_______________________ ___(c) [6 points] How does adding a transformer to the output of the power supply affect the behavior of the circuit, if the number of secondary windings on the transformer (which are connected to the circuit) is half of the number of primary windings (which are connected to the power supply)?Page 10 of
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