How do we calculate the emf and the current induced in two loops of wire, that have a portion in common between them? The specific example we had solved in class is:
The left side loop is a square and the right side loop has half the width. The magnetic field as a function of time is known, and the resistance per unit length of the wire is known.
Does a loop's being conjoined with another affect the emf induced across it? I do not understand how i can calculate the current in each wire, because there is no particular point from where the emf is induced (unlike a typical circuit with batteries). Our teacher and textbook pulled it off by assuming the induced emf in each loop to be supplied by two equivalent batteries, and using Kirchhoff's law to find the currents in each portion. Is this method correct? If not, how do we calculate the current induced in each loop?
More clarification:
Circuit diagram:
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ABEF is a square with side length $\ell$, BC = ED = $\ell/2$. The part AB has a resistance $R$, and all wires have same resistivity and cross sectional area. Now, my doubt is, will we write Kirchhoff's Loop Law equations as: $$V_1 = i_1(3R) + (i_1 - i_2)(R) \\ V_2 = i_2(2R) - (i_1 - i_2)(R) $$ or, $$\begin{align} & V_1 - V_2 = i_1(3R) + (i_1 - i_2)(R) \\ & V_2 - V_1 = i_2(2R) - (i_1 - i_2)(R) \quad\quad\text{?} \end{align} $$
Thank you!