Re: [Phys-l] induced electric field -- erratum

[David Bowman <David_Bowman@georgetowncollege.edu>]

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