Lecture Note
University:
Washington State UniversityCourse:
Physics 103 | Problem Solving for Physics 101Academic year:
2022
Views:
140
Pages:
16
Author:
Janor
F=QE + Q"Lorentz Force Equation"F = O (ve x B )In diff form :- dF = dQ (ve e xB)/I = dQ = do = I dt-2dtFrom , and 2:dF =I dt ( Ve xBeg")dF = I ( Vedt X B )& due = dldtdF = I ( dl x B )Find the force on current ( (I2) carrying conductor l2 due tocurrent carrying (I,) conductor l,.LB,I,78,XR12P,al,I'I2Line 1I,Line 2l,l2 #I,dl, X R12->H12=4T 1 R1212B12 = le I 4T dl x R12| R12B12It is total magnetic flux density at P2 due to I, CurrentDifferent ForceI,dl,duetoB12isdF12 = I2 dl2 X B12Total force on Line2F12=SI2dl2X B12^line2F12 = S I2 dl2 X / UI, di, XR124TT IR1212line1F12=leI,I2Idl2IIt,XR12X4TJline2R12F12 = j I2 dl2 X B12 = - - I2 I B12 X dl2 2linezIfBis uniformthen+12=-I2B12xS212=-- I2B12Xl2=Il2XB12=F12In general^F =Idl xB = I anFIIIIIIIBI I Sin OeB I aimi-=IlBSinO z#H12Magnetic field.xIntensity at line-2Due to line - \X(yI,H12 = I, aH ^-AI22kedline- 2line IB12 = UH12 = UI, air ^2581312 =u I ( - ax)2x(d)AI2 dl2 = Izdz azdF12 = I2 diz X B12^dF12 = I2dz az X (III(a)2T((d)dF12 = uI,I2 dz (-ay)2ndTake force on line- - 2 for h height is2thF12 = le I, I2 dz (-ay)2ndZ=OieDirection ofF12 = (-aj)ll I, I2hForce on line 22nddue to line-is towardsline - 1 Note1.dF=UI, I2h(N/mI,2ndI2F a I, I2&FxdForcebetweentwo parallel conductors carryingCurrents in the same direction is 7 tothe conductors and attractive .Force between two parallel conductors carryingcurrents in opposite directions is 1 to theconductors and repulsive.Q If Force on loop 1 is F then find force on=loop. 2 in terms of F.ZZI2=I2a2aLoop II2 =ILoop - 2aIITTaaayXXI,= IyI, = ISolB12 = UIAaH =le I ax ^2TTP2FT(2) F12 = - I2 of 312 X dl2 2 = -If 2T(2) lI ax X^ dlzF12 = -ue 2TT pazz x dlzZoaF12 = -IIa" X dy ay + ax 2 x dz az2 TTay=oz=a+ j a: x dy3ay=a 2aF12 = I2 & dlz X B12 = I2 - dizxist j. dl2 xB12y=02=aa+ iiz X B12 + I dirbi+y=a2=2aa30aF12 -- I2 S B12 xdl + of Blzxdi + j B12xdi + I B12 xdlz=3ay=o z=a y=az=a const 2=3acousta3a0N2==S2TZ 4I ax xdyay + Sa+2FTZjMAIL2TZaxxdyayyouz=a2=a ,y=a y=a,z=3aa+"II 2THZ ax X dz asZ=3a,y=0F12========= 2TI [af dy a3 + A + 39 1/6 j dy az Ay=oy=a= - "I22/1az + (4:)4F12 = - 2TT 3For Loop 1 i.e FSimilarly for Loop2= 2 TT "I2 3 A = F Note: 1. Magnetic flux density/B/= 101&B = 4 H (wb/m2)Areau = lott2. GivenBthen magnetic flux crossing open surface0= ll B.ds3. Inductance isL = NO(Henry).INO is total magnetic fluxNis number of tornsFor Single Loop N = 1 :-L=Iobservation -1. Find inductance of coaxial Cable betweene = a and b for "h" heightH I as for=25 PB=llHB -> = u as2 P0 = IIB.dsfl2ripuI ais). - (dedz as)bh= u/de2n/dzeP=a 2=0hh0=leI[emp]PZ=le Ih ln (b/a)2TT2TTP=a 0L = ofLI2TT le ln1b/a) In Henry. Q = Inductance of N-turn Solenoid Shown:-Sol = H = NI a3 Ad^B = le H = UNI azd= IIB.ds =UNI) d a3 (P de do az)a2T0= leNId fede SdpP=80=0a270= leN Id FEP 2UNIa2=(2/T)d2e=o 0=0$ = UNT (Ta2)dL=NO I = N2 henry.L= N2Rewhere RL = Reluctance of solenoidRL=& u lly lloee TTa2l= Length of conductor coill = N 1(2xa).
Static Magnetic Field
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