Puzzling inductance problem

[fhqwgads2005]

I was recently given a problem I can't quite wrap my head around. Here's the situation:

shttp://pics.bbzzdd.com/users/theman/inductorbulbs.gif

(you'll have to copy the link, - the s, into your address bar)

Oh-- and i just realized a mistake with the drawing, the dots should be x's to indicate the field is going into the page.

We have a solenoid creating an increasing magnetic field into the screen. A wire loop goes around the solenoid with two lightbulbs connected in series. The induced EMF is counter clockwise. Then, another wire is connected as shown to the top and bottom of the wire loop.

Question: what happens to the lightbulbs when the wire is connected?

My initial thought was that the light bulb on the left would turn off (short circuited) and the one on the right would get brighter.

But then I was thinking, what if the wire were just flipped over and was on the other side. Would the light bulbs then switch, and the right one would go off? I don't see why this would be true. Why should the physical orientation of the added wire affect the circuit?

 

[McLaren Rulez]

You are right in arguing that this is a symmetric situation.

I'm not entirely sure but I think nothing will happen i.e. the bulbs will continue to glow with the same intensity. Like I said, I'm not sure so I'm waiting for a concrete answer too.

 

[aneesh.mulye]

At a first guess, I'd say that nothing will happen.

Consider the closed loop consisting of the wire between the two bulbs. The rate of change of magnetic flux within that loop stays the same. Now consider the loop of wire which you have attached, and the closed loop formed by that on the left hand side of the figure. The flux passing through that is zero, and the rate of change of flux passing through it is also zero, so the attachment of the wire should do nothing.

(Note: This is simply what I remember off the top of my head. It has been more than four years since I studied this in high school, and I (regrettably) haven't touched physics since.)

 

[fhqwgads2005]

The problem is though, that the attached wire offers a path of lesser resistance through which the current can flow, instead of through one of the bulbs. I think I might actually try and build this soon and see what it actually does. This is a very strange situation indeed.

 

[rdl]

I can understand your confusion with this puzzling inductance problem. It seems like a simple circuit, but the addition of the wire and the changing magnetic field adds a level of complexity.

First, let's clarify some terminology. The solenoid is creating an increasing magnetic flux, not just a magnetic field. This is important because the changing magnetic flux is what induces the EMF in the wire loop. The direction of the induced EMF is determined by the right-hand rule, which states that if you point your thumb in the direction of the changing magnetic flux, your fingers will curl in the direction of the induced EMF.

Now, when the wire is connected to the top and bottom of the wire loop, it essentially creates a parallel circuit with the two light bulbs. This means that the current will divide between the two branches, with more current flowing through the branch with less resistance. In this case, the light bulb on the left will have less resistance since it has a shorter path to the wire, so it will receive more current and get brighter. The light bulb on the right will receive less current and get dimmer.

In terms of the physical orientation of the wire, it does not affect the circuit. The direction of the induced EMF will still be counter-clockwise, and the current will still divide between the two branches in the same way.

I hope this helps to clarify the situation. It's important to remember that inductance is a complex concept and can lead to unexpected results in circuits. It's always best to approach these problems with a clear understanding of the underlying principles and to carefully consider the effects of changing variables.