PHYS 211 Final, Fall 1995

tee oe raven : AMIR an CSIVEnE y in ‘ LiBbapy | OF Betey Physics 211 Feb. 6, 1996 Physics Department FINAL EXAM Time 2 hours Don’t forget to write your name, your 1.D.# and your section on your booklet, Part A_30 min. 20 marks Al) A small water droplet has a diameter of 4 um. If it carries a charge of I2e, a)-what is the strength and direction of the uniform electric field that will just balance the gravitational force acting on the droplet? b)-If the magnitude of the electric field is then increased to three times its previous value, how will the droplet behave compared with its behavior in the total absence of the electric field? Given: e = 1.6x10° C, the density of water is 1g/cem’, Take g=10 m/sec”. 15 marks A2) A current of 2.00 A flows in a copper wire of 1.00 mm? cross section. How long doe. it take an electron to travel 10 cm in this wire under these circumstances ? (Assume that each Cu atom contributes one conduction electron). pou = 8.92 g/em®, More = 63.5 g/mol. and Na= 6.02x10” . 15 marks A3) A toroidal coil is wound with 4000 turns of wire. The average radius of the toroid is 10 cm and the diameter of the coils is 1.5 cm. A second coil of 400 turns is wound over the first. a)- What emf is induced in the second coil if the current in the 4000-turns coil is changed at a rate of 25 A/sec? b)- Discuss also the sense of this induced emf. Part B 30 min. 15 marks _ B1)- An electron half-way between two fixed protons on the x-axis, is in stable equilibrium and executes simple harmonic motion after a shght displacement along the y-axis. Find the restoring force on the electron and deduce its natural frequency in terms of its mass m and charge e and proton-proton separation d. ‘ ‘ B2)- A’cylindrical capacitor has radii a<b, length L, and carries a charge q. _ a) Find.an expression for its capacitance. _ b)Calculate the electrical energy stored ifa =4.4 mm, b = 5.0 mm, “E= 5.0 om, q=6.0 WC and (Ane, y'=9 x10" N.m7/C? . . tp 20 marks B3)- Four long parallel wires forming the corners of a square, side a, run -perpendicular to the page and carry equal currents i each into page. . a): Find the magnetic field at one corner due to the currents at the other corners. ™ b)}-Calculate the magnetic force per meter exerted by & on the wire of that corner if i=2.0A,a=500em, pt =4nxx 107 T.nV/A . Part C_30 min. 15 marks C1)- Two identical raindrops, each carrying surplus electrons on its surface to make a net charge -q on each, collide and form a single drop of larger size. Before the collision, the characteristics of each drop are the following : a) surface charge density o, , b) electric field £ , at the surface, c) electric potential V, at the surface ( where V=0 at r= 0). For the combined drop , find these three quantities in terms of their original values. (Hint: use the fact that the volume is conserved). 20 marks C2)- An a particle ( q = +2e, m = 4.003 u) travels in a circular path of radius 4.5 cm in a magnetic field with B = 1.2T . Calculate a) its speed, b) its period of revolution, c) its kinetic energy in eV, and d) the potential difference through which it would have to be accelerated td achieve this energy. (u=1.661x10™g, e= 1.60x10""C). 15 marks C3)- At t =0, a source of emf, £ = 500 V, is applied to a coil that has an inductance of 0.80 H and a resistance of 30 Q. a)- Find the energy stored in the magnetic tield when the current reaches half its maximum value. b)-How long after the emf is connected does it take for the current to reach this value? Part D_30 min. 16 marks - D1)- A uniform conducting sphere of radius (a) carries a charge (+q). It is placed at the center of a spherical conducting shell of inner radius (b) and outer radius (c). The outer shell carries a charge of (-q). Find: a)- E(r) within the sphere ( r<a ). b)- E(r) between the sphere and the shell. ( a<r<b ). c}-E(r) outside the shell (r>c). d)- Determine the charges which will appear on the inner and outer surfaces of the shell. 18 marks : : D2) A 2500 Q resistor is connected in series with a 100 pF capacitor, a 100 V battery and a switch. The capacitor is initially uncharged. The switch is closed at t=. At what rate is the battery delivering energy to the circuit at t=0.5 sec ? 16 marks D3)- A solenoid with 1000 turns per meter has an iron core with the magnetization curve shown in the figure below. For a By field of 1.2x10° T (Wo = 412x107 N/A’): a)- Estimate the permeability constant Km ? b)-Determine the current through the windings of the solenoid. 7} B, in units of 10° T