电磁学参考公式(英文).pdf

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1、Formulae:1.The electric field at a point on the perpendicular bisector of a uniformly charged thin rod:E 2.The electric field at a point on the axis of1)A uniformly charged thin ring:E sin020 xqx223 240(R x)2)Infinite plane:E 20 x113)A uniform annulus of charge:E 2220 x2 R2x R124)Infinite charged ro

2、d:E 20 xQ40r25)A thin spherical shell:E outside,E 0inside6)An insulating sphere:E keQrinsideoutside,E 2r307)Infinite cylindrical shell:E outside,E 0inside20rR28)A infinite cylinder:E outside,E rinside20r2013.Gausss Law:eEdS S0qin4.For the electrostatic field:E dl 0(any closed path)LThe electric pote

3、ntial:VPrefPVVVEdl;Laplaces operator:E xiyjzkq40(R2 x2)1/21)The electric potential at a point on the axis of a uniformly charged thin ring:V 2)Electric potential due to a point charge:Vpkqqr40rQ40R;VoutQ40r3)A thin uniformly charged spherical shell:VinVsurf5.The work done by the electric field force

4、:W12 q(V1V2)U1U26.The electric polarization of the isotropic dielectric:P 0r1E 0eEThe surface bound charge density on the surface of dielectric:Pcos PenPdS qinSThe electric displacement：D 0E PFor the isotropic dielectric:D 0rEGauss s Law aboutD:Dds q0insCalculation about electric field when dielectr

5、ic existsCalculation about electric field when dielectric exists q0DdS q0D D E E P 0r1E P Pen7.Capacitance of1)An isolated conducting sphere:Csphere 40R2)The Parallel-Plate capacitor:C00Sd;with dielectric:C rC03)The Spherical CapacitorRa,Rb:C0 40RaRb;with dielectric:C rC0Rb Ra4)The Cylindrical Capac

6、itorRa,Rb,l:C020l;with dielectric:C rC0lnRblnRabQ QV C 5)Calculation about the capacitor:QE dS EV EdlCaV8.Parallel combination of capacitors:C Series combination of capacitors:Ci11CCi1 Q2112CVQV9.The energy stored in a capacitor:U 2 C221E22dVThe energy stored in the electrostatic field:Ue0E Vuniform

7、uedV VV2210.The magnetic force that acts on a chargeq moving with velocityv v:F qv BThe magnetic force on an arbitrarily shaped wire carrying currentI:F Idl BL11.Motion of a charged particle in a magnetic field1)Ifv/B,F 0,uniform linear motion mv2R2m2)Ifv B,Bis uniform,uniform circular motion:R,T Bq

8、vBqThe torque on a current loop when the loop is placed in a uniform external magnetic field:pmB ISenB0Idl er12.The Biot-Savart law:dB(valid only for steady currents)24r13.CalculateB1)A distance ofr from a straight wire segment carrying currentI:B Infinite1 0,2:B 0Icos1cos24r0II;One end is infinite1

9、,2:B 02r4r22)The magnetic field on the axis of a circular current loop:B The centre of the loopx 0:B 2 R x0IR222320I2R;far from the loopx :B 0IS2x33)The magnetic field on the axis of a solenoid:B The solenoid of infinite length(LR):inside2 0,1:B 0nIat the end2 0,1outside:B 00nI2cos2cos1:B 20nI214.Ga

10、usss law in magnetic field:BdS 0S15.Amperes law:LBdl 0Iin(valid for any steady current)16.The general form of Amperes law:17.Faradays Law of Induction:i LBdl 0Ic Id0E jc0dSStdmNd,induced current:Ii mdtRdtt2N12Induced quantity of electricity:q Itdt t1RdmBi dS EinduceddlstLdt18.Motional emf:motionalBv

11、 dlr119.Magnetization of isotropic magnetic medium:MB0rSurface bound current density on the surface of magnetic medium:20.Magnetic-field intensity:Hj M enBB0MFor isotropic magnetic medium:H0rAmpere s law aboutH:LH dl I0in21.Mutual-inductance:M N221N112I1I2dI1dtMutual-induced emf:2 MSelf-inductance:L NISelf-induced emf:L LdIdt12LI222.The energy stored in the magnetic field of an inductor carrying a currentI:U 21BThe energy stored in the magnetic field:：U u BHdVdVdV BB22VVV23.0 4107N/A208.851012C2/(N m2)19e 1.6010C