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106-20093-MT2 (1)

# 106-20093-MT2 (1) - PROBLEM(1(25 points The parallel plate...

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Unformatted text preview: PROBLEM (1) (25 points) The parallel plate capacitor having plate area A = 0.1 m2 and separation d = 15 cm is connected to a 60-V battery. A dielectric plastic sheet (K = 2) of the same area (A) but 60 V thickness 1:: = 6 cm is placed between the plates. (Take 80 = 9 x 10‘12 C2/N. m2. (a) (7 pts) Find the capacitance of the arrangement. } wt» éxi’o"ﬂ astic sheet. ............... (4'5 (d) (6 pts) Assume that the battery is disconnected, find the work required to puli the dielectric sheet out of the region between the plates. Phys 106 Second Mﬁemﬁﬁ" "\$5,"? U! r:— {ii’iﬁiﬂaigﬁﬁ PROBLEM (2) (25 points) A hollow cylindrical resistor with inner radius r1 and outer radius Q, and length L, is made of a material whose resistivity is p. (a) (12 pts) Show that the resitance is given by R: L111”; 2711', r1 for current ﬂows radially outward- Wq Lkmm e ij it“ AViL-ei 3' \NL“ e R F0254" w A‘ M cl 1Q“)? clux at J“ Ax M k éi’lﬁ‘m aim-,9; ﬁxmwmdo , T \w. car-{ox .3 [(4 "blimp {\de-sle t5 ”tit FL . ”War ("as We. {3% ex \ullew L3 iii/ﬁnial. wet. 121‘ is?“ M "km “0"“; . W‘ASJV vAKtLS R 7: HI .9 '1‘ all "sixes ‘\$ \I\‘L\\3 : f (b) (8 pts) Evaluate the resistance R for such a resistor made of carbon whose inner and outer radii are 1.0 mm and 1.8 mm and whose length is 3.0 cm. Resistivity of carbon: p = 3 X 10’5 Elm. be: (GNWLsA :- 11? HMJ’JLM 9 Q” 13m. (\li} MM) An (’3 ‘ti 15135 K“: “1 W631. (c) (5 pts) What is the resistance in part (b) for current flowing parallel to the axis? J12,“ 9&de rewﬁii am, (Liana?) "\on; OWNS . I W [Liﬁy'ﬁi 3’“? ix 2‘: ?§ L? Q1Q1\3’5ws§'1 i\ :- “tt Us” 1“”) Km: (”ML \ Phys 106 Second Midterm Examination Page 4 Saturday, 31 ~July, 2010 PROBLEM (3) (25 points) Assume that the capacitor in the circuit is initially uncharged and the switch S is suddenly closed at in 0. Take R1 = R2 : R3 2 R. Express your results in terms of R, E and C. (a) (7 pts) Determine the current on each resistor at t = 0 and f a 00_ M ____M___ “Mme... J \$32. me» Q ‘ [WWW-WEEK ﬁt.“ L..- MW. F“ “:3 f“ 2n“;d:a:r‘ (b) (7 pts) Write the Kirchhoff‘s rules for each loop and obtain a differential equation of charge q(t) accumulated on the capacitor at time if (during the charging of the capacitor). Kigimzﬁ3 “" lﬂ’ﬂFQ r" W... ‘3‘.“ ~ 31%. m J “‘12) 3 re“ a“ mag : Eﬁ- 1: g t’fa 1’” ‘1 gem N. 12:. ﬂ 3% + R 2. M; (c) (6 pts) Solve the equation obtained in part (b) and find (10), the charge in the capacitor as function gt time t. .. ...°E~ ﬁg i" l. ”2:. was at; {I % :1 ﬁg: CK macaw {ESQ kjtf 3: Eﬂﬁe 5,th 3 K {1 2“ o (it?) a {1* or! at 3 K e. We m. eta??? 36-6. g c e “x aWwWVW m. 72.. 53‘ a I? Fig- Phys 106 Second Midterm Examination Page 5 Saturday, aleuly, 2010 PROBLEM (4) {25 points) A square loop of wire with side 3 lies in the xy plane. The loop carries a current I as shown in the figure. There is a uniform magnetic field 17?: 50} along the +3) axis. {See the figure. Answer the questions in terms of the parameters given in the questions, I, a, B0, v0, express the vector quantities in unit vector notation.) (a) (6 pts) Find the magnitude and direction of the forces acting on the side 1 and side 2 of the loop. Side 1 and side 2 are shown in the figure. '3 . "Tl Sin/er: szfarx-god] Sic/€21 12:0 (b) (6 pts) Find the magnitude and direction of the torque acting on the loop for the position shown in the figure. ............ '--'i w rt 2/? X 8 “I“ A 2 ' ~ 6 1 Q“ E) Razed ) "'" a u ' '5‘— —— Ea 3; l C ”1"“ 3 (c) (7 pts) How much work must he done by an external agent to turn the loop from the initial position shown in the figure to a final position so that the magnetic dipole moment will be along the Ay axis. (d) (6 pts) Suppose the loop is removed, that means ignore the loop. A proton of charge +e moves with initial velocity 3 : V0} along the +x axis into the uniform magnetic field 3': .51); stated in part (a). Find the magnitude and direction of the electric field to be applied in the region so that the proton moves Without deflection. Phys 106 Second Midterm Examination Page 6 Saturday, 31-July, 2010 ...
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106-20093-MT2 (1) - PROBLEM(1(25 points The parallel plate...

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