# Direction of induced current

1. May 5, 2011

### SaraF

1. The problem statement, all variables and given/known data
This is a question from the Princeton Review of AP physics B, 2011 edition. A small circular loop of wire (radius r) is placed on an insulating stand inside a hollow solenoid of radius R. The solenoid has n turns per unit length and carries a counterclockwise current I. (The magnetic field within the solenoid is shown as pointing into the plane of the page.) If the current in the solenoid is decreased at a steady rate of a amps per second, determine the induced emf and the direction of the induced current in the loop.

2. Relevant equations
B = uonI. E = -d(BA)/dt

3. The attempt at a solution
I determined the equation for the EMF induced in the small loop correctly. I had a problem with the direction of the current. By the right hand rule, the current should be clockwise, and that is the text's correct answer. However, by the same right hand rule, I would expect the counterclockwise current in the solenoid to produce a magnetic field pointing out of the plane of the page, not into it.
Initially, I thought that the current in the small loop would be counterclockwise, because that is the direction specified for the current in the solenoid. Since the solenoid current is decreasing, the current induced in the ring would oppose that decrease, and therefore be in the same direction as the current in the solenoid, ccw. Now I am confused as to how a ccw current in the solenoid could even produce a magnetic field pointing into the plane of the page, as that conflicts with the right hand rule. I'm hoping that someone can clear up this confusion for me.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. May 5, 2011

### supratim1

the answer will be Counter-clockwise, if the current is decreasing.

3. May 6, 2011

### SaraF

Thanks, I wondered if that was the case. But that implies that a decreasing clockwise current is the same as a counterclockwise current. That is hard to reconcile with the image of electrons moving through a wire...one pictures a decreased "flow" rate but no change in direction. I realize that the flow of electric current in a wire is not really the flow of electrons from point A to point B (given the collisions between electrons and atomic nuclei, etc)...so that makes we want to understand better what is happening when electric current flows through wires. I wonder about the relation between induced current (requires change of magnetic field) and the magnetic field created by a "steady" current in a wire. Is there, actually, something changing in the current that "induces" a magnetic field? (i.e. is there some sort of reciprocity between electric current and magnetic field that works both ways?)

4. May 7, 2011

### supratim1

you would need to study maxwell's equations to understand it. also study about electron drift.

5. May 8, 2011

### SaraF

Thanks. I will do so. I figured that electron drift had something to do with it.