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I am given the following conducting track, where on its right side there is a conducting rod with mass $m$ and length $a$ which is free to slide on it. There is a constant magnetic field throughout space $\mathbf{B}=B_0\hat{z}$ where $\hat{z}$ is perpendicular to the frame and goes outwards from the page. At time $t=0$ there is no charge on the capacitor and the rod is moving at a velocity $v_0$ to the right.

I am asked to find the induced EMF on the closed path and the force on the rod at time $t$ given that the velocity of the rod is $v(t)$ and the current through it is $I(t)$.

I'm having difficulty with this problem since the induced EMF that would result from the initial velocity of the rod would itself induce a magnetic field that will oppose the original magnetic field so as to oppose the change in the flux, and that induced magnetic field will, in turn, induce a correction to the EMF which will also induce a correction to the induced magnetic field and so on, seemingly ad infinitum. The magnitude of the force on the rod is given by $F=aIB$. My problem here is also that the induced magnetic field should affect the force acting on the rod.

Now, I checked the published answer to this problem and it seems that they completely neglected the effect of the induced magnetic field in this problem, both when finding the force acting on the rod and in finding the induced EMF. My question is, why is this valid?

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It seems common in textbook problems to ignore the effects of the induced magnetic field. The flux through the current loop depends on the radius of the conducting wire and is hard to compute. The people writing these sorts of questions try to "simplify" by assuming that you would not think of this effect. In this way they inadvertently penalize the people who actually think deeply aboutwhat is going on.

I tell my own students that when doing exam problems you have to understand the physics, but you must also make a mental model of the mind of the examiner so as to answer the question they think they have asked, rather than the one they have actually asked.

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  • $\begingroup$ Thanks, that's a good piece of advice! The problem with publishing answers which ignore such effects without stating it explicitly is that it makes some students (e.g. me) think they're going crazy, or that they're missing something obvious. $\endgroup$
    – Ofek Aman
    Aug 17 '20 at 19:55
  • $\begingroup$ Perhaps I could have taken the fact that they don't give the initial distance between the rod to the parallel wire (the leftmost wire) as a hint of them wanting me to ignore the effects of the induced magnetic field, at least in finding the force on the rod, since the expression for the additional magnetic field due to the current in the left wire on the rod would depend on the distance between them. But it is all very confusing when it isn't stated explicitly. $\endgroup$
    – Ofek Aman
    Aug 17 '20 at 19:56

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