шпора 2010, 2ой семестр (Ташлыкова-Бушкевич) [5353 вопросов] / 17 векторн потен поля

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$>@<0;L=>, 5A;8 v  25:B>@=>5 ?>;5, 25:B>@=K< ?>B5=F80;>< =07K205BAO 25:B>@=>5 ?>;5 A B0:>5, GB> v=4825@35=F8O @>B>@0 A

A;8 A O2;O5BAO 25:B>@=K< ?>B5=F80;>< 4;O ?>;O v, B> 87 B>645AB20

4825@35=F8O*(4825@35=F8O @>B>@0 )=0

(4825@35=F8O @>B>@0 @02=0 =C;N) A;54C5B

4825@*v=4825@35=F8O*(4825@35=F8O @>B>@0 )=0

B> 5ABL v 4>;6=> 1KBL A>;5=>840;L=K< 25:B>@=K< ?>;5<.

;O ;N1>3> A>;5=>840;L=>3> 25:B>@=>3> ?>;O, C4>2;5B2>@ONI53> >?@545;Q==K< CA;>28O<, ACI5AB2C5B 25:B>@=K9 ?>B5=F80;.  G0AB=>AB8, 53> ACI5AB2>20=85 7028A8B >B >1;0AB8, =0 :>B>@>9 >?@545;5=> ?>;5  2 A;CG05 <=>3>A2O7=>9 >1;0AB8 ?>B5=F80; 28E@52>3> ?>;O >1KG=> =5 ACI5AB2C5B.

4=8< 87 A?>A>1>2 70?8A8 C@02=5=89 0:A25;;0 O2;O5BAO D>@<C;8@>2:0 2 B5@<8=0E 25:B>@=>3> 8 A:0;O@=>3> ?>B5=F80;>2. 5:B>@=K9 ?>B5=F80; 22>48BAO B0:8< >1@07><, GB> <N0 H=B=rot A (2 A8AB5<5 !).



@8 MB>< C@02=5=85 divB =0 C4>2;5B2>@O5BAO 02B><0B8G5A:8.

rot E=-dB/dt

rot(E+dA/dt)=0

E=-grad D8 - dD/dt

8A?>;L7CO rot rot A=grad div A- div+divA, C@02=5=8O 4;O 25:B>@=>3> 8 A:0;O@=>3> ?>B5=F80;>2 <>6=> 70?8A0BL 2 2845

div A- grad(divA+(1/c*c)dD8/dt)-1 d^2A/c^2 dt^2=-<N0j