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\^€Y Name */ I / t> out" , Fall2012 Phlzsics 22 Exarn 3 - Chapters 26, 27 .28 Do all your work in the space provided. If the work is not shown, then credit will not be given. Express your Emswer to three significant figures, unless indicated otherwise. Please underline or draw a box around your final answer, and include the correct units with your answers. L. a. Write Kirchoff's loop equations for each of the simple loops. Take the loop currents to be h, lz -"8 and Is, as shown. Sirhplify the equations by combining like terms. Do not solve. (9) . +-Vol\ *Vgf__* z+, I3 -- O th tt I 40e) *70I,* \ool-,-'frTl=-O Is -40 I t';tTu+\5"\=too 100 v 7 b. Write the equation that allows you to find Ves. Do not solve. (4) Ve* - -1oIr +"o3 u T t3 2. A simple circuit is shown to the right. a. If an ideal ammeter is inserted at point B, then what will its reading be? (3) ^ tDo t- srrL +- 7Dl I roo =ta \>- o = D. g-)) A 7 b. If an ideal voltmeter is connected between points A and B, then what will its reading be? (3) V+a = il2 L =- toQrbv) +t ;1l* = :=:-\ 1 A galvanometer is used in a real ammeter and a real voltmeter. The resistance of the galvanometer is 10 ohms. In the ammeter, the shunt resistor is 1.2 ohms and in the voltmeter the series resistor is 820 ohms. c. What is the reading on the real ammeter when inserted at point B? (No voltmeter connected.) a*^-r.*e-b,e-^ -l7D t [=f,orL Io' -- L_1 d. L 1)-(,DJ \1'o1 5L IL 5e *r- ! l.oJ la-ti =- lDo /\ 5 reading on the real voltmeter when connected between points ammeter connected.) (5) \Atrhat is the $7o Rv 1- t0+?7/o: -.ct,-) v, \f*<)w A andB? (No rt-'-s I st-a'^- \ , 'oLt)D) : +l,lL SL r-*\--l / r-t tz P2 Ttto 'ot*ru -+io -}" *r'-:\ ^\0o {- ''t1.lL i t\ L3 V*r= c-c- I -"1D I- --o T -- b. klt 10',' .17,-'n- | Lt-i 10? f : c-* -r1o};O $.ssl At 'lu S tb An switch is located between points A and B in the circuit. a. SI?ST Find the potential difference Vee. (6) .-lL +-loo f -rl f ?ot2 f '-o aot)'\ =' , T = D.DlblA Vo, = Too{g)-1+l *voo[.ottr) =- -L Jr V,)1 V* =- *-1,?t* "-==#-F The switch is now closed. Find the magnitude and direction of the current flowing through the switch. (8) TooT\ - 74u I-_ _ooll rs\fl, I )f \Voo = = l :-\ \.;" -)^ t ?oO -)z{o \ --o 5bo looo + lboo \5-oo oo - +ado \ +DD *-- Il F Dopo ArV9 ? tr switch 4. switch 2 1 In the circuit showrL at time f = 0, switch 1 is closed. a. Find the voltage across the capacitor at t = 1.2 msec '1 a-fter switch 1 is closed. (6) Ltr - v,= ; v""-) | a loo l\-u 1 V, [Du ( a \DD (t 100 YY<i'1 volts - ulrt.o 1 o*)= 0,&f(oL zo(+X T= +r E^--- ,-'-5]z'-&- - ['rr ) t -. r-l) 2- ll, b (r- # p At this time (t = 1,.2msec), switch 1 is opened and switch 2 is closed (done simultaneously). Find the magnitude and direction of the current flowing through the 200 ohm resistor 2.0 msec later. (6) Vr:VrL -?- =Vr,,rtVr* "WoL t-t'l) f = vv/' - V, -f)-- = :2.U 1bu ' 11. t 'l oo -W = 0_1[ RL , _, Li':' 10r-, (t nr" ) -- -L,? f lo -3 -1' -'2^?vto n - otrT U =- 0- llr\ Iurto) ; *,\ )r, rL lv An electron (q = -t, m"= 9.1L x 10-31 kg) has an initial ,L velocity of ao= 4.0 x 105/ m/s (see diagram). A uniform electric field, E = -2000 uniform magnetic field E= iN/ C' and a i', 3'0110{ ur"present. If you were to look at the motion of the electron from along the r-axis, which type of motion would you observe (1. or 2)? (2) b. \zVhat is the value of the radius of the circle whicht:"**Tf"'n' r--.:;a in =ffi n.i" o, l \ (* l, fl + I c. How far along the x-axis will the electron travel when it undergoes one complete revolution? rt'r,lt = V,fl Xlo ?( = v-t urLt- . zn-[z- 1r ) = X= o -v\A,t\Xlo 'n)(''\ * L,+i t,ttr rlo DD] + rt" t "1 ? fi) qe.u ''xl" ) "^^- il A long, straight wire carries a current Il. A rectangular loop carries a current 1z in a clockwise directiorL and the loop is in the same plane as the wire. a. &h \ l+,- f )rY Find the magnitude and direction of the force on loop segment 1-2 due to the magnetic field of the Iong wire. (4) I,= f ,.;8, ,i1o' = IrrL I Et = _____> rl [ -o [D'i-\t, \ F r-b. Y Find the magnitude and direction of the force on loop segment 4-L due to the long wire. (6) Lr--r d{- h F= i1,t" --r.,-L\t D1 " \ >TY) D,-.' W-l% -t l3 JD r*r(= M, ), L- A G-hT *> D+V'2 /l t* \ v c. Find the magnitude and direction of the torque acting on loop due to the long wire. (Careful!) (3) +- )n'r t"l --f* '. Lo'a-\ "") T'- O F 1F a t] 7. A circular loop of wire with a radius R, and carrying a current I lies in the y-z plane. a. Start with the Law of Biot-Savart and derive an expression for the magnetic field on the r-axis at a distance r from the center of the loop. (6) B? =- 1), =-O J9^=J3e*(9-=H Ll.-tLlt rl-" -2 Y-t R -1?n i rlP vtrY Dr= DF= I,,U - :.. 1^z > L*'vt) \ t- Prt"b !" b. The diagram below shows the loop in cross-section. Draw small compasses at each of the five (5) dotted positions showing the orientation of the compass and label the north-seeking end oI the compass. (5) y \ rl v 8. The diagram shows the end view of two long wires whose lengths are parallel to the z-axis. They carry currents I in opposite directions, and are placed a distance D to the left and right of the \"; \( --\- h,- v&\ origin. a. , Find the magnitude and direction of the magnetic field at point P, a distance y above the origin on the vertical axis. (6) E= - \)Lr;0-* Ro)*$ D D f ur' tA:=:\g- i.Hfu-) ry-- uLrTrvT)W,wcI-> RT r o"r) \ f Y A third wire, carrying a current l out of the page, is positioned parallel to the first two wires - passing through point P. Find the magnitude and direction of the force on a length L of the and third wire. (4) e t--- tr : !-LBe o*7oo Irz .tr{- , .l rr- [u*+3 ) l') +_, sirl",4 -- lD