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I came across this question while studying for a Physics test, with the corresponding answers posted below it.

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But isn't the direction of the induced current as a consequence of Lenz's law such that the new magnetic field it induces opposes the original magnetic field, not that it must cause an opposition of motion or force (although this is sometimes a logical consequence)? I have only understood Lenz's law in the context of loops of wire such that an electromagnet (in the style of a solenoid) is created and thus finding the direction of the current is easy. Because by this logic wouldn't the direction of current on each side of a loop be the same, meaning the current can't flow through the loop?

Any help is greatly appreciated.

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The conservation of energy is an interesting perspective to see this problem. But I believe it is correct.

The flux of magnetic field lines through the loop is increasing as more of the loop enters the region of the magnetic field lines. Lenz's law says that to oppose this, a current is induced such that its magnetic field points in the opposite direction.

In this case, the external field is into the page, so the induced field should be out of the page. Then by the right-hand rule, the current should flow counter-clockwise (that is, flowing upwards on the right segment of the loop).

The force felt by this current due to the external field is in the direction of $\vec{I}\times\vec{B}$. By the right-hand rule again, if the current is flowing up and the external magnetic field is into the page, the force is to the left.

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  • $\begingroup$ I agree with everything you've written, but I think you've misunderstood my question. What I am asking is what happens when rather than having a loop of wire, a single straight conductor is passed through the magnetic field? I now realise this is not the best example given your interpretation of the question, but I am asking what happens if you consider the conductor as being not part of a loop, and disconnected from a circuit. $\endgroup$
    – ajax2112
    Nov 3, 2020 at 5:52
  • $\begingroup$ Ah, I see! I'm terribly sorry. In that case, there would be no induced current, and thus no force. This is because a straight line has zero area, so the flux of the field lines through a zero-area surface is automatically zero. $\endgroup$ Nov 3, 2020 at 22:08
  • $\begingroup$ Thank you for that. That makes a lot of sense. $\endgroup$
    – ajax2112
    Nov 4, 2020 at 4:27

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