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1 1

2 1.. ( )

3 ( ) ( ) (A) E icb φ Et = + cdiva ct (H3) (B) ( ) ct ct ' ctct ' + ' = ' ct ' + ct ' i( ') (H3,H18) 3

4 (i) cosh Ψ = cosh ΘcoshΩ sinhψ sinhθ sinhω cosh Ψ cosh Θ cosh Ω = sinhψ sinhθ sinhω tanhψ = tanhθ+ tanhω+ dω i dτ 4

5 (ii) 1 dcτ = ( dct d ) cosh Ω sinhω ( ) (iii) ( ) (iv) ( ) 5

6 ( ) 6

7 (I) ( ) (A) E icb φ Et = + cdiva ct (H3) (B) ( ) ct ct ' ctct ' + ' = ' ct ' + ct ' i( ') (H3,H18) 7

8 E (A) t φ = + ct cdiva ( ) (H8,H18) φ E t = 0 + divca = 0 ct ( ) E t φ = divca = ct 0 1 (i) ( ( ) χ φ' = φ + + div cχ ct c χ c A ' = c A g a d χ + i o t c χ ct 8

9 E φ = + ct (A) t cdiva (ii) j j F= qe+ E + cb c t c ( q = 0,back building) ( ) 9

10 (i) j c c B df ( :I 1 ds 1 ) µ ( I ds I ds ) µ ( I ds ) I 1 1 = π 3 4π 3 ds ( : I ds ) df µ ( I ds I ds ) µ 1 = π 3 4π 3 ( I ds ) I 10 ds 1

11 (ii) j c E t f f ( I 1 ds 1 ) µ ( I ds ) I ds µ ( I ds ) I ds = + + 4π 4π ( I ds ) µ µ ( I ds ) I ds ( I ds ) I ds = π 4 4 (H5) π 11

12 (I) ( ) (A) E icb φ Et = + cdiva ct (H3) (B) ( ) ct ct ' ctct ' + ' = ' ct ' + ct ' i( ') (H3,H18) 1

13 (B) ( ) 1 (i) ( ) ( ) ct ct x ct ct ct + x y + iz = = = y ( x y z) y iz ct x z 13

14 (B) ( ) (ii) ( ) ct ct ' ct + x y + iz ct ' + x ' y ' + iz ' = ' y iz ct x y ' iz ' ct ' x ' ctct ' + ' = ct ' + ct ' i( ') 14

15 ( ) ( ) (A) (H3,H18) (B) E t (H3,H18) (C) E t (H5,H18) 15

16 (A) (ii) = (E t : ) H3,H Et φ ct = ic E B ca φ Et = + divca ( ) iii(1) ct ca E = gadφ ( ) iiiiiiiiiiiiiiiiii() ct cb = ot ca ( ) iiiiiiiiiiiiiiiiii(3) 16

17 (B) (i) = (E t : ) H3,H ρ + ct E t ε 0 = ic E B j ε c cb ot E + = 0 ( ) iii(1) ct divcb = 0 ( ) iiiiii() Et ρ dive + = ( ) iiiiiiiiii(3) ct ε 0 E j ot cb gadet = ( ) iii(4) ct ε0c 17

18 (C) + q F E t t = ic j F E B c (iii) = (E t : ) H5,H18 j j Ft = qet + Ei cb ( ) iii(1 c c j j j F= qe+ Et + cbi( qcb E) ( ) iiiiiiiii( c c c ( ) 18

19 ( ) ( ) (A) ( ) H0 (B) H9,H0? ( ) (C) ( ) (( )) 19

20 (A) ( ) 1 (i) ( ) ( ) e φ = 4 1 πε 0 e, A= 0 ( ) M U = GM c 0

21 (A) ( ) (ii) ( F (, u q ) 0 c c ) = qe= 4 q 0 πε 0 ( ) M f ( ) u t e ( ) u U Gm M = m = 0 ( ) 0 c t c u t ( ) c ((!!))

22 ( ) ( ) (A) ( ) H0 (B) H9,H0? ( ) (C) ( ) (( ))

23 (B) ( ) 1 (i) = (E t g t : ) ( ) Et ( 0) e = q 0 ct = E icb( = 0) 4πε 0 0 ( )H9,H0 + get ( = 0) M G ct = 0 ge icgb( = 0) c + + 3

24 (B) ( ) i) ( ) = (E t g t : ) ( ) u q F E icb( = 0) u q 0 c t + ( 0) 0 F E t t = c = ( ) H9,H0 ( ) + ut Et ( 0) m0 ft g = c = f ge icgb( = 0) u m 0 c 4

25 (B) ( ) 3 (iii) = (g t : ) (i) (ii) ( ) H9,H0 ut + g ( 0) m0 ft Et = c = g icg ( ) f E B = 0 u m 0 c + + u M m t 0 G ct c = c u m 0 0 c 5

26 (B) ( ) 4 (iii) ( ) ( ) + + ut M m0 f t G ct c = f c u m 0 0 c u m t 0 c + 0 G = M c ( ) u m 0 c M ( ) m u G t 0 c = c M ut M u ( ) m0 + i ( ) m0 c 6 c

27 (B) ( ) 4 (iv) ( ) H9,H0 ) Gm0 M ft = ( ) u ( ) iii(1) 3 c Gm0 M Gm0 M f = ( ) u ( ) ( ) () 3 t i u iiiiiiii 3 c c ) dct Gm0 M = ( ) uiii(1) 3 dτ c d Gm0 M Gm0 M = ( ) u ( ) ) () 3 t i u iiiiiiii 3 dτ c c 7

28 ( ) ( ) (A) ( ) H0 (B) H9,H0? ( ) (C) ( ) (( )) 8

29 (C) ( ) 1 (i) ( ) z d x= y = z = sin sin cos θ θ θ cos sin φ φ x φ θ dθ sinθ dφ y 9

30 (C) ( ) (ii) ( ) H9,H0 dct M G d dct = (1) ct dτ dτ dτ d M dct 1 dθ 1 dφ = + + θ dτ dτ dτ dτ d dθ M dct dφ dφ ( ) = i θ θ i dτ dτ dτ dτ dτ d dφ M dct dφ dθ ( sin θ ) = i θ i dτ d τ dτ dτ dτ G ( ) {( ) ( sin ) } () 3 G { cos }( sin ) (3) θ G { cos }( ) (4) φ 30

31 (C) ( ) 3 (iii) θ Ω ( ) H9,H0 π = :, : i Ω dct M G ddct = (1) dτ dτ dτ d M G dct 1 dφ dω = ( ) + {( cosh Ω ) ( ) } () 3 dτ dτ dτ dτ d dω M G dct dφ dφ ( ) = ( sinh Ω )( cosh Ω ) (3) dτ dτ dτ dτ dτ d dφ M G dct dφ dω ( cosh Ω ) = ( sinh Ω )( ) (4) dτ dτ dτ dτ dτ 31

32 (C) ( ) 4 ( ) (i) cosh Ψ = cosh ΘcoshΩ sinhψ sinhθ sinhω cosh Ψ cosh Θ cosh Ω = sinhψ sinhθ sinhω tanhψ = tanhθ+ tanhω dω i dτ 3

33 (C) ( ) 5 ( ) (ii) 1 dcτ = ( dct d ) cosh Ω sinhω (iii) ( ) (iv) ( ) 33

34 34