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I'm having trouble in applying Lenz's Law in the following problem.

Find the direction of induced current. Note-w.r.t means with respect to time, B with an upward arrow means it increases with respect to time.

I could find the induced current in the outer loop to be anti-clockwise as per Lenz's Law but my textbook says that the inner loop (smaller circle) will also have anti-clockwise current induced and the connecting wire will have no current induced. How is this possible?

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The directions in the loops will be same.(the answer above says why and you should figure most of it out yourself for practice). The interesting part is why there is no current in the conneting wire. From faradays law, we know that if a circuit(mathematically defined as a contour of integration $C$) has non Zero rate of flux change through it, there is an induced emf in the chosen contour $C$. But note that in the figure, you cannot draw a non-self intersecting loop which includes the connecting wire. Or in other words, there exists no closed contour $C$ such that $w \in C$ where $w$ ,denotes the connecting wire. Thus there cannot be an emf across itz ends and therefore no current.

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  • $\begingroup$ Could you explain without the countour of integration? I'm just a high-school student. A little help would be great. $\endgroup$ – user38863 Jan 11 '17 at 21:01
  • $\begingroup$ Don't worry much about that. At this level a non rigororus explanation of a closed contour is just a closed path along which the line integral B.dl of ampere-maxwell eqn is performed. In most simple textbook problems, we take a circular loop and ocnsider the current through it. If the curent distribution is symmetric, integral of B.dl can simply be written as B.2pi.r and hence proceed.vjust remember contour is a path along which the integral is taken. $\endgroup$ – Lelouch Jan 12 '17 at 4:21
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According to Lenz's Law both loops will have anticlockwise current induced because magnetic flux is increasing for both (in the same direction).

enter image description here

Also, in closed loops in changing magnetic fields, electric potential is "not defined" at a point due to circular electric field lines. Increasing or decreasing magnetic field produces circular electric fields. There is also no general potential between the two loops, like there is no general potential between two batteries. Connecting one terminal of the first with one of the second battery brings them to the same potential, and only then, you will have a potential between the unconnected terminals.

Also, you know that any current carrying wire has circular magnetic fields around it. In this case if the connecting wire carries a current then the changing external magnetic field will tend to intersect with the magnetic fields of the connecting wire. But magnetic field lines normally do not intersect.. So it is reasonable to assume that the no current flows through the connecting wire.

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