PHS 212 Final, Fall 2004

NDU PHS 212 - Electricity & Magnetism Faculty of Natural and Applied Sciences Final Exam ‘ Department of Sciences i . — Pe fu? Solve all problems (13 points each) i= iS ( A ~q) = K hat Ie ue ; aA : "a Se ‘ : ‘ee Sk 1. Acharge Q is torbe divided into two parts (Q—g) and g . What is the relation of g to q_-if the two parts, placed a given distance apart, are to have a maximum Coulomb repulsion? ‘ — . j arbi ae 2. A plane slab of thickness Td has a uniform volume charge density p . Find the magnitude of the electric field at all points in space both (a) inside and (b) outside the slab, in ; seit GH: . therdistancameannl frown thesmedlon vlan rr oftheslab. 7 A(< opt More Yet y se =o We We Bees mus P ite Fy 2A: > f iA +k 4, as fon lows JERK = Claws ba en Kher Gora = Cs & (EY B 3. Consider two widely separated cond Ba spheres, 4 ‘and D5 the Second. having owicesdhe diameter of the first. The smaller sphere initially has a positive charge q and the larger one is initially uncharged. You now connect the spheres with a long thin wire. a) How are the final potentials v, and V, of the spheres related? b) Find the final charges 4, and a, in terms of q: VV, | Aah. KGt- K&L fia A. ; 4. When 115y is applied across a 9.66—m - long wire, the current density is 1.42 Alem? Calculate the conductivity of the material. ' Qn= 24, Agr ts 3 5. Two long, straight wires, each carrying current i, are perpendicular to one another as shown here. If the wire are free to move, what happens? 6. The figure shows a cross section of a hollow cylindrical conductor of radii g and jp , carrying a uniformly distributed current j; . a) Using the circular Amperian loop shown, verify that p(y) fortherange p<;<q is given by Hi rp: 2n(a’-b’) +r . «b)-Test this formula for-the special cases of -=g,p=p , and b=0 - 7. A wire having the form shown here carries current i. Find the magnitude and direction of the magnetic field at P. ~ ~ | Mm. Tf. ' 8. The long wire in the figure below carries a current ip . The square . . - ..wire loop with sides /‘moves to the right with speed v ig Lz L a. Find the emf induced in the loop as a function of the distance x ; between the long wire and the left side of the loop. | b. What is the direction of the current in the loop? i, 9, The two capacitors, C,=2.2uF,C,=3.4uF + in the circuit illustrated below are initially. charged to a 220-V potential difference. At t= 0, the switch is closed. Find an expression for the current through the inductor, -=41mH » asa function of time. 10. Two long parallel wires, each of radius g ,whose centers areadistance g apart carry equal currents in opposite directions. Show that, neglecting the flux within the wires, themselves, the inductance ofalength , of sucha pair of wires is given by ul = L= al Ne in d-a T a