Static E field [Archive] - Physics Forums

Danny

May16-04, 12:58 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>The coulomb field of a point charge at rest is the starting point of\nthe study of electricity and magnetism. Let us assume that at time t1\nthe field\nis E(t1). How is it that the field at time t2, where t2 > t1 continues\nto be\nE(t1) ? Ofcourse Maxwell\'s theory or Coulomb\'s law simply gives the\nanswer but\nmy question is, how is this information, that the charge is at rest\ncommunicated to the point at which the E field is being calculated?\nWhat goes\non so that the point "knows" that it has to have the same value of E ?\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>The coulomb field of a point charge at rest is the starting point of
the study of electricity and magnetism. Let us assume that at time t1
the field
is E(t1). How is it that the field at time t2, where t2 > t1 continues
to be
E(t1) ? Ofcourse Maxwell's theory or Coulomb's law simply gives the
answer but
my question is, how is this information, that the charge is at rest
communicated to the point at which the E field is being calculated?
What goes
on so that the point "knows" that it has to have the same value of E ?

Hephaestus

May17-04, 05:05 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nphys_tutor2004@yahoo.com (Danny) wrote in message news:<486dd4de.0405152111.60a72271@posting.google. com>...\n> The coulomb field of a point charge at rest is the starting point of\n> the study of electricity and magnetism. Let us assume that at time t1\n> the field\n> is E(t1). How is it that the field at time t2, where t2 > t1 continues\n> to be\n> E(t1) ? Ofcourse Maxwell\'s theory or Coulomb\'s law simply gives the\n> answer but\n> my question is, how is this information, that the charge is at rest\n> communicated to the point at which the E field is being calculated?\n> What goes\n> on so that the point "knows" that it has to have the same value of E ?\n\nI assume it\'s the spooky "action at a distance" issue you want\nresolved?\n\nIt\'s possible to describe the time evolution of electromagnetic fields\nin a\ncompletely local manner. In fact, Maxwell\'s equations in differential\nform\nis exactly that. Since dB/dt is zero, we get curl E(x) = 0 and div\nE(x) =\nrho(x)/e_0. Note that there is no dependence of E(x) on any fields or\nvalues not at x itself. curl E = 0 and div E = constant, with E being\ninitially the field produced by the point charge, (messy math omitted)\nnecessarily implies E is constant.\n\nOf course, you\'ll say that you already said that. But here\'s why it\'s\nimportant: *if* the point charge were to move, for a while the same\nsituation would still be in effect, meaning E would still be constant.\nE has no way of knowing that the point charge moved; there\'s no B\nfield\nor rho, so it still stays constant. No action at a distance! Of\ncourse,\nthis situation eventually changes: from the point source outward, the\ninfluence of its movement is being felt locally, and these changes\npropagate\noutward at c as a consequence of Maxwell\'s laws. For times t > |x -\nx_0|/c,\nholding curl E = 0 and div E = constant no longer means that E is\nconstant ...\nE must change to preserve these equations! But everything is still\nlocal: E\nis not adapting to the position of the point charge, it is simply\nresponding\nto *local* changes in the environment, namely the values and\nderivatives of\nE(x) and B(x) at that particular point.\n\nIt\'s similar to the way that an object in orbit doesn\'t "know" what\norbit it\nis in ... at each point in time it simply moves in accordance with the\nforces\nthat are acting on it.\n\nDoes that help?\n\nHeph\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>phys_tutor2004@yahoo.com (Danny) wrote in message news:<486dd4de.0405152111.60a72271@posting.google.com>...
> The coulomb field of a point charge at rest is the starting point of
> the study of electricity and magnetism. Let us assume that at time t1
> the field
> is E(t1). How is it that the field at time t2, where t2 > t1 continues
> to be
> E(t1) ? Ofcourse Maxwell's theory or Coulomb's law simply gives the
> answer but
> my question is, how is this information, that the charge is at rest
> communicated to the point at which the E field is being calculated?
> What goes
> on so that the point "knows" that it has to have the same value of E ?

I assume it's the spooky "action at a distance" issue you want
resolved?

It's possible to describe the time evolution of electromagnetic fields
in a
completely local manner. In fact, Maxwell's equations in differential
form
is exactly that. Since dB/dt is zero, we get curl E(x) = and div
E(x) =\rho(x)/e_0. Note that there is no dependence of E(x) on any fields or
values not at x itself. curl E = and div E = constant, with E being
initially the field produced by the point charge, (messy math omitted)
necessarily implies E is constant.

Of course, you'll say that you already said that. But here's why it's
important: *if* the point charge were to move, for a while the same
situation would still be in effect, meaning E would still be constant.
E has no way of knowing that the point charge moved; there's no B
field
or \rho, so it still stays constant. No action at a distance! Of
course,
this situation eventually changes: from the point source outward, the
influence of its movement is being felt locally, and these changes
propagate
outward at c as a consequence of Maxwell's laws. For times t > |x -x_0|/c,
holding curl E = and div E = constant no longer means that E is
constant ...
E must change to preserve these equations! But everything is still
local: E
is not adapting to the position of the point charge, it is simply
responding
to *local* changes in the environment, namely the values and
derivatives of
E(x) and B(x) at that particular point.

It's similar to the way that an object in orbit doesn't "know" what
orbit it
is in ... at each point in time it simply moves in accordance with the
forces
that are acting on it.

Does that help?

Heph

Igor

May17-04, 08:13 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>phys_tutor2004@yahoo.com (Danny) wrote in message news:<486dd4de.0405152111.60a72271@posting.google. com>...\n> The coulomb field of a point charge at rest is the starting point of\n> the study of electricity and magnetism. Let us assume that at time t1\n> the field\n> is E(t1). How is it that the field at time t2, where t2 > t1 continues\n> to be\n> E(t1) ? Ofcourse Maxwell\'s theory or Coulomb\'s law simply gives the\n> answer but\n> my question is, how is this information, that the charge is at rest\n> communicated to the point at which the E field is being calculated?\n> What goes\n> on so that the point "knows" that it has to have the same value of E ?\n\n\nAn electrostatic field is governed strictly by Gauss\'s Law, which is\nindependent of time, providing that the amount of charge enclosed by\nthe Gaussian surface does not change with time. Same surface, same\ncharge, and thus same electric field. But if any charge enters or\nleaves the given surface in a particular time interval, the field has\nno choice but to change accordingly.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>phys_tutor2004@yahoo.com (Danny) wrote in message news:<486dd4de.0405152111.60a72271@posting.google.com>...
> The coulomb field of a point charge at rest is the starting point of
> the study of electricity and magnetism. Let us assume that at time t1
> the field
> is E(t1). How is it that the field at time t2, where t2 > t1 continues
> to be
> E(t1) ? Ofcourse Maxwell's theory or Coulomb's law simply gives the
> answer but
> my question is, how is this information, that the charge is at rest
> communicated to the point at which the E field is being calculated?
> What goes
> on so that the point "knows" that it has to have the same value of E ?

An electrostatic field is governed strictly by Gauss's Law, which is
independent of time, providing that the amount of charge enclosed by
the Gaussian surface does not change with time. Same surface, same
charge, and thus same electric field. But if any charge enters or
leaves the given surface in a particular time interval, the field has
no choice but to change accordingly.