I'm a retired Physics Professor, but I admit I'm puzzled by this...

Consider two loops of wire, 2 small dipoles B and C , with a common axis z (facing each other) and (say) 30 cm apart B to C. At the speed of light, information (including a change in magnetic field) will require about 1 nanosecond to travel from C to B.

  1. Have the current on in coil B for some period of time at the start, so the B-fields at C is established in the +z-direction.
  2. Turn loop B off rapidly (fall time < 0.3 ns, say) at the same time that a current in loop C is turned ON (rapidly, rise time <0.3ns, and current in opposite sense with respect to the previous current in loop B).

  3. In this way, as the current is turned on in loop C, it is immersed in the field from loop B and therefore it receives an impulse to the right, in the +z-direction.

However, loop B will be "off" (and open so no effective eddy currents) when the "return" field from loop C arrives.

Thus, loop C (which is free to move) will experience a force giving it momentum in the +z direction (to the right), whereas loop B will not experience a force to the left. It seems that Newton's Third Law is violated.
(The question can also be posed in momentum terms, but I chose to consider forces and the Third Law. )


1 Answer 1


In electromagnetism you can find millions of examples of apparent momentum non-conservation. They are all explained by the fact that the electromagnetic field itself carries momentum, and only the total momentum of all matter plus the EM field is conserved.

  • $\begingroup$ So, to conserve momentum in this specific case and since loop C is pushed to the +z direction, the EM field must carry momentum in the -z direction, is that correct? $\endgroup$ Aug 6, 2011 at 13:27
  • $\begingroup$ That's correct. $\endgroup$
    – petergreat
    Aug 6, 2011 at 16:48
  • $\begingroup$ Fortunately, as you have said, the timescale needed is nanoseconds if you have a table-top setup. So the apparent "violation" of Newton's 3rd law is tiny in everyday life, even if EM field momentum is not taken into account. $\endgroup$
    – petergreat
    Aug 6, 2011 at 23:05
  • $\begingroup$ Now, petergreat, would you please look then at my follow-on question in which I consider the "momentum in the -z direction", by placing a third loop to the left of B... "3 loops..." Thanks. $\endgroup$ Aug 7, 2011 at 2:50
  • $\begingroup$ So this would be an electromagnetic thruster? $\endgroup$
    – endolith
    Aug 15, 2011 at 5:54

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