PHYS 211 Final, Summer 1996

. 3) 1S.marks BO Physics 211 September 2 , 1996 Physics Department Final Exam Time 2 hours t rit 1) 10 marks A certain charge Q is to be divided into two parts (Q-q) and q. What is the relation of Q toq if the two parts, placed a given distance apart, are to have a maximum Coulomb repulsion? pt Bis Pacers [" EEARY Or ned 2) 10 marks A neutron is thought to be composed of one “up” quark of charge #? e and two “down” quarks each having charge -e/3._ If the down quarks are 2.6 F apart inside the neutron, what is the repulsive electrical force between them? (1 F = Fermi = 105m) A charge per unit length of A is uniformly -- distributed along the upper half of an infinite insulating rod and a charge per unit length of -X is uniformly distributed along the lower half, as shown in the figure. Find the electric field E at P situated at a distance r from the point O. 4) 15 marks The spherical region a <r <b carries a charge per unit volume of p=A/r, where A is a constant. At the center (r = 0) of the enclosed cavity is a point charge q. What should be the value of A so that the electric field in the region a < r < b has constant magnitude ? : 5) 15 marks Knowing that the potential in the space is given by V(x,y,z) = € (x’ + y’) Where ga is aconstant. Find the electric field Z and sketch the line fields in the space. 6) 10 marks Find the equivalent capacitance between a and b of the circuit shown where all the capacitors are identical. | ot 1 yyy {4} 7) ark Show that the plates of a parallel-plate capacitor attract each other with a force 2 q 2€ given by F= . Where q is the charge and A is the area of the plate. a 8) LO marks When 115 V is applied across a 9.66 m long wire, the curtent density is 1.42 Alm’. Calculate the conductivity of the wire material. 4R 2R 9) 15 marks Calculate the current i if E=12 V th and R = 3Q. (Hint, use Ae>Y transformation). 3R 5R aw, __| | 10) 15 marks E|! A long , rigid conductor, lying along the x axis, carries a current of 5.0 A in the (-x) direction. A magnetic ficld B is present, given by B = 3% + 8x?., with x in meters and B inmT. Calculate the force on the 2.0 m segment of the conductor that lies between x = 1.2 mand x = 3.2 m. 11) 1S marks | Two long parallel wires a distance 2d apart carry equal currents i in the same direction, into the plane of the figure. —_ Derive an expression for the magnetic PR field B at a point P on the line connecting —-i@-- - !-- ~@io- the wires and a distance x from the point s d ¢ midway between them. Plot B against x. ; iV ‘ 12) 1S.marks el : a) Find an expression for the energy density as a function Y of the radial distance r for atoroid of rectangular cross section. b) Integrating the energy density over the volume of the toroid, calculate the total energy stored in the field of the toroid. 13) 15 marks Consider the circuit shown: Ss, - Sr ‘Si. L Cc R 88 {{—-— Describe qualitatively and quantitatively what happens if one of the switches is closed and the other two switches are open, starting with switch S, closed , then S2 and 53? 14) 15 marks In an LC circuit with L = 52.2 ml] and C = 4.21 pF, the current is initially a * maximum. How long will it take before the capacitor is fully charged for the first time? 15) 15 marks Which one of the following circuits resonate? What is its resonance frequency? 52 S00.Q 5000 2 — Good Luck