A conductor of known volume (V) passes a uniform magnetic field(B)with a constant velocity (v) the conductor is a source of induced EMF, a power source to a circuit. The induced EMF can be calculated via formula: ϵ=−vBL A diagram of this:

enter image description here

The conductor has resitance(R) and induces current equal to:

I=VR Excluding all other factors that would retard the motion, what would happen if the magnetic field span is reduced? Span; meaning It covers a smaller volume(i.e area) of the conductor at the same magnetic field strength as before, moving at the same velocity:

enter image description here

From the motional EMF formula, if all the vairbales are the same (v,B,L) it should induce the same ϵ. The only difference is the induced current correct? How would I go about calculating it?

EDIT: There is a connection to the conductor via an exterior circuit from the top and bottom, complete connections(not partial) but fully connects the top surface and bottom.

  • \$\begingroup\$ Where and how are you making your connections to the conductor? Top and bottom, sides, or front and back? Are the connections static or do they slide across the conductor as it moves? Are the connections inside the field? \$\endgroup\$ – bigjosh Aug 10 '15 at 3:48
  • \$\begingroup\$ @bigjosh complete connection of the top side and bottom(not partial, but complete). Connections static, and not inside the field, sorry for not clarifying the detail. \$\endgroup\$ – Pupil Aug 10 '15 at 3:50
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    \$\begingroup\$ Looking at some of your other questions, I'd strongly recommend the book Matter and Interactions. It does a great job explaining the interactions between the magnetic and electric fields. \$\endgroup\$ – bigjosh Aug 10 '15 at 4:09

Assuming that you are connecting your circuit to the top and bottom of the conductor and assuming an ideal conductor with no resistance, the circuit would not get any power because the voltage induced in the part of the conductor that was inside the field would immediately flow though the part of the conductor that is not inside the field. No current would flow through the circuit, only an eddy current inside the conductor.

enter image description here

Note that the induced eddy current will generate a magnetic field that opposes the motion of conductor relative to the original magnetic field B. You can see a fun example of this here..


If you had a non-ideal conductor, then the amount of power that makes it into your circuit depends on the resistance of the conductor and the location of the connection points between your circuit and the conductor. If the connections were made as shown in the figure above, then you would expect to see the current though the circuit grow as the field got closer to the connection points in the center of the conductor, and then fall off as the field continued past them. Note that the current though the circuit would be small compared to the case where the conductor was completely contained within the field because much of the current would flow though parts of the conductor not inside the field.

  • \$\begingroup\$ I've edited you're image here: i.imgur.com/glXEYUH.png If you consider the connections(top/bottom) to be equal to the width of the conductor the induced EMF should be of value. From a Physics stand point, it seems that there is induced EMF look here: physics.stackexchange.com/questions/197770/… \$\endgroup\$ – Pupil Aug 10 '15 at 13:44
  • \$\begingroup\$ I am not sure I see the difference. I think the point here is that the voltage potential is only generated inside the part of the conductor inside the field. Any part of the conductor that is outside the field will act like conductors do and conduct current if there is a voltage potential across it. Make sense? \$\endgroup\$ – bigjosh Aug 10 '15 at 17:56
  • \$\begingroup\$ It might help to think about individual charges. A single charge feels a force when it moves though a magnetic field. The force causes the charges to move until so many of them pile up on one side of the conductor that the repulsive electric force cancels the force trying to move them. This generated electric field is the source of the voltage. \$\endgroup\$ – bigjosh Aug 10 '15 at 17:59
  • \$\begingroup\$ I think my main focus is the existence of the a voltage throughout the conductor's surface like so: i.imgur.com/nDpzJ4F.png?1 Where the whole bottom part would be postive(if measure with voltmeter at any point at the bottom and top). It makes sense for current to flow in the direction of eddy's but I think we can agree that there is an induced EMF? And it is equal to the one covering the magnetic field because of vBL? \$\endgroup\$ – Pupil Aug 11 '15 at 7:18
  • \$\begingroup\$ Here are some other diagrams similar to this problem, just a battery instead of the induced EMF from the motion(pretty much the same concept two voltage source) :i.imgur.com/B4q0Cvp.png and i.imgur.com/RjpxUDJ.png ... there will be an induced EMF equal to the battery(blue rectangules) on the top/bottom side if connected to a volt-meter. \$\endgroup\$ – Pupil Aug 12 '15 at 5:21

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