# How is the current induced in this circuit?

Rectangle FBCE is the conducting wire. The circle is where magnetic field exists.The perimeter of the circle is NOT a conducting wire. R1,R2,...are different resistances.

If the magnetic field(B) is increased at a constant rate will there be a current produced ? If so, in which direction ?

According to Lenz's law, if an induced current flows, its direction is always such that it will oppose the change which produced it. Since the magnetic field is changing, I am almost sure there will be some kind of current flowing in the circuit which would oppose the increase in magnetic field. But I couldn't figure out how or in which direction should it flow, so as to effectively oppose the increasing magnetic field. I have considered the situation where Current flows through FBCE and that would somehow oppose the changing magnetic field. But, I don't think that's correct.

I also tried to observe the circuit in a simpler form wherein I put a cell in the part of the circuit where the emf is produced due to changing flux. It generally works great when the whole circuit is inside the zone where the field is changing. That approach isn't working here. Does anybody have an idea on how current should flow ?

Please answer the question if you are very sure about the answer you are giving. Having a wrong concept would be terrible for me at this point of time.

If magnetic field B is coming out of the page and increasing, then the current in the conducting loop FBCE will flow clockwise.

Take a look at segment EF. If the current is flowing clockwise from E up to F, then the right hand rule tells us that the magnetic field generated by that current will create a circular magnetic field around the segment that goes out of the page on the outside of the loop and into the page inside the loop...

...same goes for all the other segments, with the net result being that the current circulating clockwise in the loop will generate a magnetic field that goes into the page inside the loop, which will resist the magnetic flux that is increasing out of the page.

There is another rule of thumb that gives the same answer

With the thumb of your right hand point in the direction of decreasing flux, your fingers will curl around in the direction of the electric field.

Note that in this rule, your thumb points in the direction of decreasing flux. This reflects the negative sign in Faraday's law. Also note that the decreasing flux could mean a field pointing out of the page increasing in time, or a field pointing into the page and decreasing in time.

No current will flow though segment AD.

Since AD does not enclose the changing flux, it does not experience any emf along its length so no current flows though it. All of the forces on its charged particles are perpendicular to its length.

You might think that the current flowing around the outside loop FBCE might create a voltage across AD and that might cause a current to flow though it, and this would be true in a battery-powered circuit because the battery creates an electric field that drives the current around the loop. But in this case, there is no electric field between A and D- they are at the same voltage potential. This is a hard concept to grasp when you are used to looking at battery driven circuits. Imagine this circuit sitting flat on a table. The charges are uniformly distributed around all of the conducting elements so there are no voltage differentials and no electric fields. Now you start increasing the flux. This causes a force on every charge particle that is curly and clockwise. This force pushes the particles around the perimeter loop. They are now moving, but their density has not changed. They are still uniform density so there is still no electric field anywhere. Make sense? (Note that this really is only accurate if the loop is circular, but this does not effect our questions here because the rectangular loop is symmetrical around R1.)

Since you are asking such a great question, I think you'd really enjoy the following resources:

1. Matter and Interactions. Explains this stuff in terms of fields and forces and the movement of charged particles, which is very different from the way electronics is typically presented and helps explains stuff that doesn't make sens when you only think in terms of traditional circuit theory. Completely dissolves the false distinction between static electricity and circuit theory.

2. Electricity and Magnetism (Berkeley Physics Course, Vol. 2). Explains this stuff in terms of special relativity. There is no magnetic field, just the normal electrical field as felt by moving particles due to Lorenz transformation. Mind blowing and makes everything finally come together including the deep reality of what electromagnetic waves actually are. Note you can likely find the first edition of this book for free on the web. The 3rd edition is expensive, but includes more problems with solutions which are great for self-study.

3. Lec 16: Electromagnetic Induction. Covers the above question and ends with a demonstration that will likely keep you awake thinking for many nights. Be prepared to watch this over and over!

• EF is not in the field, how can a current be induced in it? Also, is a current in generated along AD? No field lines are cut. Surely the only currents are eddy currents in AD circulating in the plane of the circle and producing field lines downwards into the circular area. – Chu 7 mins ago
– Chu
Commented Sep 11, 2015 at 18:21
• Will AD have current flowing through it ? Commented Sep 11, 2015 at 18:29
– Chu
Commented Sep 11, 2015 at 18:44
• No current will flow though AB. Reason explained above. Commented Sep 11, 2015 at 23:56
• Thanks, it was really helpful. This question was closed on Physics SE as they thought it was a homework. But i knew it was a good question. Electrical SE is better! @bigjosh Commented Sep 12, 2015 at 11:02

Any current that flows must produce a field that opposes the changing flux that created it. How is it possible for a flux to be generated downwards in direct opposition to the increasing flux arrows pointing upwards? Only AD is in the field so any flux that is generated can only come from current in this conductor. But current along the length of AD will not do the job because that will produce a circular field around AD with zero overall opposition to the main flux. Therefore ...

• The emf that drives current around FBCE is generated by the changing flux inside the field as drawn EVEN THOUGH THE MAGNETIC FIELD AT EVERY POINT AROUND FBCE IS ZERO! Yep, this stuff is not intuitive until you grapple with the relativistic interpretation where all the forces are really electrical in moving frames. Even then, this stuff is hard to get your head around. We are so lucky that people like Eisenstein came up with the relativistic explanation otherwise it would be completely baffling! Commented Sep 11, 2015 at 18:54
• @bigjosh, please explain how the current is generated through conductor AD
– Chu
Commented Sep 11, 2015 at 19:23
• No current is generated though segment AD. There is no electric field along its length, so nothing that would cause current to flow. Commented Sep 11, 2015 at 19:47
• @bigjosh so, how is the current generated in EF, and all the other segments, given that none of them are in the field?
– Chu
Commented Sep 11, 2015 at 20:12
• There is a non-coulomb curly electric field that surrounds a changing magnetic field. You do not need to be inside the magnetic field to feel this curly electric field, and in fact it exists even where there is no magnetic field anywhere at all (imagine the moment a changing magnetic field passes though zero). Hopefully this link will help explain! Commented Sep 11, 2015 at 20:20