[전자기학] 전자기학 McGrawHill 연습문제풀이7장

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목차

7.1.Let V =2 xy 2 z 3 and =.Given point P (1 ,2 , 1),find:

7.3.Let V (x,y )=4 2 x +f (x ) −3 y 2 in a region of free space where ┭ v =0.It is known that both
E and V are zero at the origin.Find f (x )and V (x,y ):

7.5.Given the potential field V =(A┭ 4 +B┭ −4 )sin 4 ┵ :

7.7.Let V =(cos 2 ┵ )/┭ in free space.
a)Find the volume charge density at point A (0 .5 ,60 ◦,1):Use Poisson ’s equation:

7.9.The functions V 1 (┭,┵,z )and V 2 (┭,┵,z )both satisfy Laplace ’s equation in the region a <┭ <b ,
0 ●┵<2 ┪ , −L <z<L ;each is zero on the surfaces ┭ =b for −L <z<L ;z = −L for
a <┭ <b ;and z =L for a <┭ <b ;and each is 100 Von the surface ┭ =a for −L <z<L .

7.11.The conducting planes 2 x +3 y =12 and 2 x +3 y =18 are at potentials of 100 Vand 0,
respectively.Let =0 and find:
...

본문내용

7.9.The functions V 1 (┭,┵,z )and V 2 (┭,┵,z )both satisfy Laplace ’s equation in the region a <┭ <b ,
0 ●┵<2 ┪ , −L <z<L ;each is zero on the surfaces ┭ =b for −L <z<L ;z = −L for
a <┭ <b ;and z =L for a <┭ <b ;and each is 100 Von the surface ┭ =a for −L <z<L .
a)In the region speci fied above,is Laplace ’s equation satis fied by the functions V 1 +V 2 ,
V 1
−V 2 ,V 1 +3,and V 1 V 2 ?Yesfor the first three,since Laplace ’s equation is linear.No
for V 1 V 2 .
b)On the boundary surfaces speci fied,are the potential values given above obtained from
the functions V 1 +V 2 ,V 1
−V 2 ,V 1 +3,and V 1 V 2 ?At the 100 Vsurface (┭ =a ),No for all.
At the 0 Vsurfaces,yes,except for V 1 +3.
c)Are the functions V 1 +V 2 ,V 1
−V 2 ,V 1 +3,and V 1 V 2 identical with V 1 ?Only V 2 is,
since it is given as satisfying all the boundary conditions that V 1 does.Therefore,by the
uniqueness theorem,V 2 =V 1 .The others,not satisfying the boundary conditions,are
not the same as V 1 .

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