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さなえわしあし
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1 F(r)=QE(r) Q ρ( r ') 3 E= ke 3 ( r r ') d r ' V r r'

2 () Er () = Fr Q E E x y Ez ρ = x y z ε E E z y Ex E E z y Ex =, =, = y z z x x y A A x y Az diva = x y z A A z y A A x A z y Ax rot A =,, y z z x x y ρ dive = ε rote = dive =

3 Q E r = ke r 3 ρ r r dive = kq e div 3 r x y z = kq e x r 3 y r 3 z r 3 x 1 x 1 = x xr r x x( x y z) 1 3x = 3 5 r r 3 3 3/ x y z x y z = x r y r z r 3 5 r r 3 5 r r 3 5 r r = E E x y Ez dive = x y z =

4 rote = rote x E E z y z y = kq e y z 3 3 y r z r zy yz kq 3 3 = e 5 5 r r = (3115) rote = E x ρ r = ke x x d x x V r r' ( ') 3 3 ( ') r ' V ρ () r = x Ex ( x x') = ke ρ r x V x [( ') ( ') ( ') ] x x y y z z 1 3( x x') 3 = ke ρ( r') d r' V 3 5 r r' r r' 3 ( ') d ' 3/ r yzv, dive = rote = ρ () r = r r = φ φ E = φ (31)

5 ρ( r ') 3 φ = ke d r ' V r r' E = φ div E = ρ / ε ρ div( φ ) = ε (33) div φ φ φ = x x y y z z ( φ ) φ φ φ = x y z (34) = (35) x y z (33) φ ρ = (36) ε f ( ) rot f = (37) rote = (36) ρ = φ = (38)

6 (38) E = φ L V(L)=E L x V(x)=E x E=E V()= x yz x =, L < x < L ρ = x = L φ ( L) = V x = φ () = yz yz, φ x φ( x) 1 yz, yz,

7 d φ = dx φ ( x) = ax b ab, φ ( L) = V φ () = Vx φ ( x) = L E = φ (333) φ V φ φ Ex = =, Ex = =, Ez = = x L y z x dive = rote = φ( xy, ) φ(, ) ρ(, ) xy = xy x y ε x φ(, xy) φ( xy, ) φ( x xy, ) φ( xy, ) = lim x x x x x

8 φ ( xy, ) φ ( x xy, ) φ ( xy, ) x x φ(x x,y)φ(x,y) φ(x,y)φ(x x,y) x x x x x φ( xy, ) φ( x x, y) φ( x, y) = lim x x x x x φ(, xy)/ x φ(, xy) x φ( xy, ) = x φ( xy, ) φ( x xy, ) lim x x x x φ( xy, ) xφ( xy, ) xφ( x xy, ) x x x

9 xφ( xy, ) xφ( x xy, ) x 1 φ( x x, y) φ( x, y) φ( x, y) φ( x x, y) = x x x 1 = [ φ( x xy, ) φ( x xy, ) φ( xy, )] ( x) φ( xy, ) 1 [ φ( x xy, ) φ( x xy, ) φ( xy, )] x ( x) φ( xy, ) 1 [ φ( xy, y) φ( xy, y) φ( xy, )] y ( y) x = y = h 1 1 h h ρ( xy, ) = ε [ φ( x hy, ) φ( x hy, ) φ( xy, )] [ φ( xy, h) φ( xy, h) φ( xy, )] φ(, xy) φ( x h, y) φ( x h, y) φ( x, y h) φ( x, y h) h ρ( x, y) φ( xy, ) = 4 4ε φ( xy, ) φ( xy, ) = x y φ( x h, y) φ( x h, y) φ( x, y h) φ( x, y h) φ( xy, ) = 4 (, xy) ( x h, y)( x h, y) (, xy h)(, xy h)φ

10 φ(, xy) φ (, xy) φ( xyz,, ) φ( xyz,, ) φ( xyz,, ) = x y z φ( x hyz,, ) φ( x hyz,, ) φ( xy, hz, ) φ( xy, hz, ) φ( xyz,, h) φ( xyz,, h) φ( xyz,, ) = 6 x x x, y y y 1 1 MN, h x x = Nh, y y = Mh 1 1 x = x ih ( i =,1,,, N ), y = y jh ( j =,1,,, M) 1 1 (, ij) φ(, ij)

11 φ( i 1, j) φ( i 1, j) φ( ij, 1) φ( ij, 1) φ(, ij) = 4 φ( i 1, j) φ( i 1, j) φ(, i j 1) φ(, i j 1) h ρ(, i j) φ(, ij) = 4 4ε h ρ(, i j)/4ε B fx=(ab1cb3)/4

15 φ( xy, ) φ( xy, ) Ex( x, y) =, Ey( x, y) = x y φ(, ) φ(, ) φ(, ) φ(, ) Ex( x, y) x x y x y, Ey( x, y) x y y x y x y (, i j) ( 1, ) (, ) (, 1) (, ) (, ) φ i j φ ij, (, ) φ ij = = φ ij Ex i j Ey i j h h Ex (, i j) E (, i j) y x y 361

16 36 8 Sub drawfield() n = 19 m = 9 Call DrawRectangle(7, 1, 33 * n, 33 * m) For i = 1 To m For j = 1 To n dy = Cells(4 j, i) * 4 dx = Cells(44 j, i) * 4 Call drawline(7 3 * j, 1 3 * i, 7 3 * j 5 * dx, 1 3 * i 5 * dy) Next j Next i End Sub Sub drawline(x1, y1, x, y) ActiveSheet.Shapes.AddLine(x1, y1, x, y).select Selection.ShapeRange.Line.EndArrowheadStyle = msoarrowheadstealth Selection.ShapeRange.Line.EndArrowheadLength = msoarrowheadlengthmedium

17 Selection.ShapeRange.Line.EndArrowheadWidth = msoarrowheadwidthmedium Selection.ShapeRange.Line.ForeColor.SchemeColor = End Sub Sub DrawRectangle(x1, y1, x, y) ActiveSheet.Shapes.AddShape(msoShapeRectangle, x1, y1, x, y).select Selection.ShapeRange.Fill.ForeColor.SchemeColor = 9 End Sub

. p.1/14

. p.1/14 F(x,y) = (F 1 (x,y),f 2 (x,y)) (x,y). p.2/14 F(x,y) = (F 1 (x,y),f 2 (x,y)) (x,y) (x,y) h. p.2/14 F(x,y) = (F 1 (x,y),f 2 (x,y)) (x,y) (x,y) h h { F 2 (x+ h,y) F 2 2(x h,y) F 2 1(x,y+ h)+f 2 1(x,y