I am just surprised why EMF and Current are not induced in an unclosed wire. I know Maxwell's equation only defines closed integral. But it doesn't mean that it is not generated in a unclosed wire. Unclosed wire is stationary and magnetic flux is changing with time.
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2Have you ever seen a dipole antenna? If no current could be induced, it would not work... Where do you get your statement from? – Floris Feb 01 '16 at 13:34
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That means Current is induced in an unclosed wire also ? But my book says no. And any other reference books not mention this. – curious_mind Feb 01 '16 at 13:36
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3See this question. Every "open" wire has some intrinsic capacitance which allows (AC) currents to flow. – Floris Feb 01 '16 at 13:36
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Does the question I linked answer your question? Or does it leave you with further doubts? – Floris Feb 01 '16 at 13:49
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1@Floris My interpretation of the question, supported by what he reports that he read in his book, is that his question is about DC (steady) currents. Perhaps the OP can clarify the question. – garyp Feb 01 '16 at 14:21
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@garyp - maybe ; but in DC you will still induce an emf. – Floris Feb 01 '16 at 14:22
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@Floris How so? – garyp Feb 01 '16 at 14:24
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@garyp - see may answer. The diagram might explain what I mean. – Floris Feb 01 '16 at 14:33
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1Yes I am concerned only of DC Current. But in DC Why i have induced EMF? In my book it is written that : In unclosed wire you will have induced emf but current only generated in Loops. – curious_mind Feb 01 '16 at 14:33
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@HardeyPandya - you wrote your comment just as I posted my answer. Did that clear it up for you? – Floris Feb 01 '16 at 14:36
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No, Please check my comment. – curious_mind Feb 01 '16 at 14:38
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EMF induced in a straight wire moving in a magnetic field E = BvL and current induced = E/R = BvL/R – Anubhav Goel Feb 01 '16 at 14:38
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@AnubhavGoel, E=BvL is true only for regular magnetic field. Magnetic field is changing with time here. – curious_mind Feb 01 '16 at 14:39
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You did not post changing magnetic field in question. – Anubhav Goel Feb 01 '16 at 14:43
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@Floris Gotcha. EMF yes, current no. – garyp Feb 01 '16 at 14:43
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Can you explain type of your changing field – Anubhav Goel Feb 01 '16 at 14:46
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that means $\frac{dB}{dt} \neq 0$ and $A$ is constant and $\frac{dB}{dt}$ maybe a function of time. – curious_mind Feb 01 '16 at 14:47
2 Answers
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Maybe this diagram will help:
The charge carriers inside the wire will experience a force when they move relative to a magnetic field. This will cause them to be displaced in the wire - as they move, an electric field (emf) is induced in the wire that makes them want to "move the other way". When the two forces are balanced, the charges stop moving.
In an AC situation, current will keep flowing (see this question about antennas); in a DC situation, you just end up with a potential difference between the ends of the (open) wire.
The relationship between the amount of charge that flows, and the potential difference that is set up, is the capacitance of the wire. In the DC case, there will just be a transient charge flow (when the wire first starts moving) to set up the e.m.f. - once that has been established, no further current can (or needs to) flow as the forces are balanced.
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If flux is changing with time, then (depending on the geometry of the flux change) you may have "field lines coming from infinity and crossing the wire". If so, then there is a relative velocity between magnetic field and charges, and an emf is generated. – Floris Feb 01 '16 at 14:42
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Force created due to potential difference in wire balances moving charge to stop. – Anubhav Goel Feb 01 '16 at 14:53
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@Floris , you say "field lines coming from infinity and crossing the wire"... Then what is the mathematical explanation of that relative velocity between magnetic field and charge? – curious_mind Feb 01 '16 at 14:57
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As an EMF is created in wire, an electric field is set in which want electrons to come back. This counterbalance the force on electrons due to motion of wire.At equilibrium position both forces are equal. – Anubhav Goel Feb 01 '16 at 15:05
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I drew the two forces that balance - the force due to the magnetic field in the left hand diagram (red), and the force due to the electric field (caused by charge separation) in the right diagram (green). – Floris Feb 01 '16 at 15:06
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@Floris No, I am talking about changing magnetic field. Then you cannot apply Lorentz Force. – curious_mind Feb 01 '16 at 15:09
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Would this answer address your concern? Incidentally - the "wire is stationary" is something you added after we had been at this for over an hour... – Floris Feb 01 '16 at 15:11
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No, This answer not address my concern, because its about moving conductors in stationary Magnetic Field, I am asking for Vice-versa. – curious_mind Feb 01 '16 at 15:13
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The diagram below is a practical realisation of a metal bar passing through a magnetic field if the galvanometer (sensitive ammeter) is omitted.
As was explained in the answer from @Floris charges move along the bar until the electric field inside the wire is strong enough to stop further movement of charges.
Connecting a galvanometer as in the diagram gives a conducting path, an induced current flows and the galvanometer gives a reading.
Now how might this all be explained using Faraday’s law?
You would say that there is a closed loop: the bar, the galvanometer and the connecting wires with a changing magnetic flux through the closed loop and so an emf is induced.
There is no mention by Faraday where that emf resides other than in the loop.
Faraday also does not specify what the loop should be made of so it could be made of an insulator.
This then resembles the situation in the answer given by Floris – a metal rod with an insulator (the air) completing the circuit.
Now that loop made up of the rod and air can be of any size and the size of the loop will determine the rate of change of flux through it and hence the induced emf.
So you cannot say that the emf is set up across the rod or can you?
Farcher
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But in the vaccum, will EMF generate? Floris suggested me this answer : http://physics.stackexchange.com/a/9851/26969.. And I think special relativity concerns my question. – curious_mind Feb 02 '16 at 04:41