The direction of induced current and magnetic field produced

[JessicaHelena]

Homework Statement

The figure below shows a small circular loop of wire in the plane of a long, straight wire that carries a steady current I upward. If the loop is moved from distance x_2 to distance x_1 from the straight wire, what will be the direction of the induced current in the loop and the direction of the corresponding magnetic field it produces?

Homework Equations

right hand rule?

The Attempt at a Solution

I am at a total loss as to how to solve this problem (unfortunately, I'm not familiar with the concept to begin with)... I was thinking the right hand rules might help me, but both #1 and #2 rules don't seem to be much of help. I also know that E=Blv, but otherwise I am very stuck... Please help!

 

[stockzahn]

Do you know what kind of magnetic field is generated by the current in the straight wire?

 

[JessicaHelena]

@stockzahn
electric magnetic field?

 

[stockzahn]

@stockzahn
electric magnetic field?

Well, the magnetic field produced by a moving electric charge.

 

[JessicaHelena]

@stockzahn
No, I don't think I do...

 

[stockzahn]

@stockzahn
No, I don't think I do...

If you are looking in the "flow direction" of the current, a magnetic field rotating clockwise (by definition) is generated. Just search for "magnetic field of moving charge" or something similar in the internet, you will find pictures and explanations.

Secondly, a changing magnetic field induces a current in a conductor. The magnetic field strength increases, when approching to the straight wire, therefore a current is induced in the small circuit. This current of course generates a magnetic field as well (since it consists of moving charges). Now, what do you think:

1) The induced current generates a magnet field poiniting in the same direction as the "original" magnetic field of the straight wire or
2) the induced current generates a magnet field poiniting in the opposite direction as the "original" magnetic field of the straight wire?

 

[JessicaHelena]

@stockzahn
induced current generates a magnetic field pointing in the opp direction?

 

[stockzahn]

@stockzahn
induced current generates a magnetic field pointing in the opp direction?

Correct, otherwise we could create a perpetuum mobile. Therefore the (part) question in which direction the magnetic field of the small circuit points should be solved (which is?). Now the question remains, if the current is conducted clockwise or counterclockwise to generate this kind of field.

 

[JessicaHelena]

@stockzahn

The problem is I'm not really sure which direction the magnetic field was initially pointing... But since you did say in #6 that it's clockwise, I'm guessing counterclockwise... I feel like I'm mixing things up here... :(

 

[gneill]

@stockzahn

The problem is I'm not really sure which direction the magnetic field was initially pointing... But since you did say in #6 that it's clockwise, I'm guessing counterclockwise... I feel like I'm mixing things up here... :(

You should become familiar with the right hand rule for currents and magnetic fields. See the Hyperphysics web page:

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html

 

[stockzahn]

@stockzahn
I feel like I'm mixing things up here... :(

Unfortunately you are. I attached a small schemtic with an coordinate system. On the left-hand side there is the original situation from your textbook, we are looking on the xy-plane (in neg. z-direction). If we flip the picture to look on the xz-plane (pos. y-direction), we are looking along the straight wire in current direction (which is marked with an x to see that the current is conducted away from us). The samll circuit from this perspective looks like a line.

How would the magnetic field generated by the current in the straight wire look like in the second perspective (xz-plane)?

 

[JessicaHelena]

@stockzahn
so in the image on the left (textbook image), the field is clockwise since it's coming out of the page, and so the opp of that (bc of induced current) would be counterclockwise. It'd also point out of the page then? But doesn't the field already point out of the page in the original example as well?

 

[stockzahn]

so in the image on the left (textbook image), the field is clockwise

The field is clockwise with respect to the direction of the current $I$. You have to position yourself to look in the flow direction of the current (like in the picture on the right-hand side) and then you can draw concentric circles around the wire (red in attachment) - that's the shape of the magnetic field. And it gets weaker with increasing distance from the wire.

From the textbook image's point of view the field lines look like lines (like the small circuit in the right-hand side view).

It'd also point out of the page then? But doesn't the field already point out of the page in the original example as well?

So, the direction of magnetic field is indicated by the field lines with the red arrows. If you change to textbook view again: Are they pointing in or out?