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A conductor in case 1 has two separate uniform magnetic fields \$B_1\$ & \$B_2\$: enter image description here

The magnetic fields(the blue rectangles are the field regions parallel to the conductor, while X's are the field lines going into the page) both changing at the same rate over the same duration of time, inducing an EMF(\$\epsilon\$) on each part with respect to their magnetic fields.However, \$B_1\$'s change is in a way that it's induced \$\epsilon\$ opposes the other:

enter image description here

Now it's quite simple to solve, since this is not a closed loop(only focusing on EMF) the net EMF would be (A) $$ V_n = V_2 - V_1 = 0$$

However, what if I changed things in case 2, by changing the region of the magnetic field of \$B_1\$ , yet made the rate of change between the two fields the same, so that their induced EMF's are both the same: enter image description here

What is the end result here? I don't know how this affects the induced EMF's cancelling each other; they are still the same and opposing one another:

enter image description here

With that change, is this expression still true?

(B)$$ V_n = V_2 - V_1 = 0$$

If not, why?

NOTE: This is an open circuit, focusing only on the behavior of the opposing voltages, it the sake of understanding.

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Your first example can be considered as a 1-dimensional problem, since the conditions along the horizontal axis are the same everywhere.

However, your second example becomes a 2-dimensional problem, in which you need to consider how current can flow on either side of the lower narrow B field.

So no, your simple expression is no longer true.

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  • \$\begingroup\$ Well, I thought of how the second case would be, I assumed(if it we're a closed circuit) that current will flow expect in the area of \$V_1\$ \$\endgroup\$ – Pupil Sep 1 '15 at 20:54

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