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Oops!
Again it seems that I made a typo in my posted exact solution. There
was an overall sign error that negates both the E_x and E_y
components for the solution I gave in my last post. Either that or
one could have considered the solution as for the case where the
B-field is increasing at a rate of B' along the (-)z direction
instead of the (+) z direction. The sign-fixed version for B
increasing along the (+)z direction at a rate of B' is given here:
Let A == L/2 - x
Let B == L/2 + x
Let C == L/2 - y
Let D == L/2 + y
E_x = (-B'/(4*[pi]))*(A*ln((A^2 + C^2)/(A^2 + D^2)) +
B*ln((B^2 + C^2)/(B^2 + D^2))+ 2*C(arctan(A/C) + arctan(B/C))
- 2*D(arctan(A/D) + arctan(B/D)))
and
E_y = (B'/(4*[pi]))*(C*ln((A^2 + C^2)/(B^2 + C^2)) +
D*ln((A^2 + D^2)/(B^2 + D^2))+ 2*A(arctan(C/A) + arctan(D/A))
- 2*B(arctan(C/B) + arctan(D/B)))
David Bowman
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