《電動(dòng)力學(xué)(第二版)》(郭碩鴻)第一章習(xí)題

1、第一章 習(xí) 題2. (1(x y z x y z x y z f f ff u x y z df u df u df u du x du y du z df u u u du x y z df u du=+=+=+ =e e e e e e e e e(2(y x z y x z A u A u A u u x y zdA u dA u u udu x du y dA u u du z d u du=+=+=A A(3(y z x x z y y x z A u A u u yz A u A u zx A u A u x y =-+-+ - A e e e(y z x x z y y x z

2、dA u dA u u u y duz du dA u dA u u u z du x du dA u dA u u u x du y du d u du=-+-+- =e e e A3. (1 (222'''z z y y x x r -+-+-=(z y x z z y y x x e e e r '''-+-+-=(rz z y y x x r zr y r x r r r y x z y x r e e e e e e z =-+-+-=+=-'''1' 321111'rr r r dr rd r

3、r r r -=-= =-013= -=r r r 033134333=+-=+=r r r r r r r r r 1r r0=r 處44233=r r r d r S S r 因此:(r r43=r(2以下各式中a 、k 和0E 為常矢量(3'''=-+-+-=z z z y y y x x x r (0''''''= -+-+ -=zy x x x y y y x z z x x x z y y z z z y e e e r (ar r r r r a =+=+=z a y a x a z a y a x a z

4、y x z y x(ae e e r a =+=-+-+-=-+-+-=z z y y x x z y x z y x a a a z z a y y a x x a z z a y y a x x a ''''''以下推導(dǎo)所用三個(gè)公式:(+=A A A (A A A +=(u dudfu f = (r k k E r k r k E r k E r k E =c o s c o s s i n s i n0000(r k E k E r k r k E r k r k E =cos cos sin sin 00004.(1b is a vect

5、or constant Gauss Theorem(dV d d d =-b f b f S b f S b S f(f b f b b f f b -=-=(Vd dV dV -=-=f b f b f bf S f =d dV (2Stokes Theorem(=b l l b S b d d d (b b b b =+=(b S S b S b =d d d =l S d d 5.(-=dV t dV tt dt d ','''','x x J x x p (dV t z dVt y dV t x z y x -=,''&#

6、39;,''','''x J e x J e x J e(xJ x x x x x +=+=+=J e J J J J J x '''''''''' (x J x x -=J J '''' (y J y y -=J J '''' (z J z z -=J J '''' (=+=dVt dV J dV J dV J dt d z z y y x x ,'x J e e

7、 e p6.311R R R R R m m m m =+= =R m A - = =R R R m m m A 2 其中:3111R R R R R R m m m m m -=+= 0122= R R m m -=-=3R R m A 7. (1=q d S D1r r <, 0=E21r r r <<, (3132344r r r E f-=(r E 33133rr r f -=2r r >, (313220344r r r E f-= (r E 3031323r r r f -=(221r r r <<,fP -= -=-=0011D P2r r =

8、,(f f e P r r r r r r r E r P r -=- -=03231323231r r =, (01011=r E r P r e P 8.(1磁感應(yīng)強(qiáng)度2r r >, =I d 0l B(-=r J B f r r r 212202(r J B -=f rr r 221220221r r r <<, =I d l B (-=r J B f r r r 2122(r J B -=f rr r 221221r r < , 0=B (2磁化電流21r r r <<, H M M =f M J H M J 0M -=1 2r r = , M d

9、J l M =,(ff MM r r r r r r r J r J r B r M r M M n 221202222120211221211122- -=- -=-=-=-=- 1r r =, 0=M 9.f =D ,=D E(001r e =+,01e =- D D E P -= -=000011ef P -= -=-=0011D P 10.(b a c a b c b a c -=,03=rr(=-=-=- =12121212121232121031221044444L L L L L L L S L L L L d d r I I d d r I I d d r r d d I I

10、d d r r d d I I d r d I I 12211212121212l l r l l rl l r r S l l l r r l l r l l F 同理(-=123212104L L d d r I I 122121l l r F 11. (112D D D =,11DE =,22DE =+=+=22112211l lD lE l E2211l l D +=,221131l l D f f +=-=(2 (212210f =-=n D D 介質(zhì)漏電(12211E E J =, 2221E E =221122211E l l l E l E +=+=2112121122l l

11、l l E +=+=211221l l E +=211212111l l E D +=211221222l l E D +=21121211l l D f +=21122123l l D f +-=-=(2(212211221212112f D D l l -=-=-=+n D D12.(1 (01212=-E E n 1122sin sin E E = (01212=-D D n 1122cos cos D D =111D E =,222D E = 222111cos cos E E = 1212tan tan = (2 (01212=-E E n 1122sin sin E E = 0d

12、dV t =-=J S (恒定電流 (01212=-J J n 1122cos cos J J = 111222sin cos E E = 1212tan tan = 13.(1 (01212=-E E n , 01=E 0212=E n 導(dǎo)體外電場(chǎng)線垂直導(dǎo)體表面 (2 =0S J d (01212=-J Jnf 2f 3f 121- - - - - - - -+ + + + + + + + 0=2J 0112=J n 0112=E n 導(dǎo)體內(nèi)電場(chǎng)線平行導(dǎo)體表面14.(1圓柱無(wú)限長(zhǎng),D 和E 只有徑向分量,且僅為r 的函數(shù)(r D r D r =,(r E r E r = 代入t -=B E ,得:0=-tB t 時(shí)無(wú)電磁場(chǎng),0=t B 0=B ,代入t=+E H J 得:0t+=EJ (2由=q d S D 得:f E