I've been having trouble understanding magnetic flux and this problem. It states that we are given a broken wire loop, and half of the loop is placed among a uniform magnetic field that goes out of the page. The other half of the loop hangs out in a space with no magnetic field, but that half also has a broken part, so essentially disconnected. The loop is not moving and neither is the magnetic field. If we reconnected the wire loop so that it allows current to be conducted through again, would there be a current induced by the magnetic field? enter image description here

I believe that there would be no current induced, despite the fact that the broken loop is reconnected. That's because the loop is not moving anywhere, and the same amount of magnetic field lines still goes through the area of half of the loop. So, according to magnetic flux equation, where magnetic flux = change of B x A, there is no magnetic flux change, and thus no induced current. Can someone please help confirm if my thinking is correct? If there is an induced current, where in my logic/concepts am I going wrong? Thank you in advance!

  • $\begingroup$ Your reasoning is correct and your conclusion is correct. Note that changing magnetic flux through a loop would produce an emf (even if the loop were broken or made of a non-conductor or even imaginary!), though no current would flow in these cases. However in your scenario, there is neither emf nor current. $\endgroup$ Commented Apr 9, 2018 at 22:03

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This question can be addressed through conservation of energy. If the loop were moving through the magnetic field, then it would have kinetic energy, and that kinetic energy could supply the energy to create a voltage and thus a current. If the magnetic field were changing, then that again could be supplying energy. But merely connecting a wire loop isn't supplying energy, so it can't create a current.


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