The direction of induced current and magnetic field produced

In summary: From the textbook image's point of view the field lines look like lines (like the small circuit in the right-hand side view).
  • #1
JessicaHelena
188
3

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!
 

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  • #2
Do you know what kind of magnetic field is generated by the current in the straight wire?
 
  • #3
@stockzahn
electric magnetic field?
 
  • #4
JessicaHelena said:
@stockzahn
electric magnetic field?

Well, the magnetic field produced by a moving electric charge.
 
  • #5
  • #6
JessicaHelena said:
@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?
 
  • #7
@stockzahn
induced current generates a magnetic field pointing in the opp direction?
 
  • #8
JessicaHelena said:
@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.
 
  • #9
@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... :(
 
  • #10
JessicaHelena said:
@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
 
  • #11
JessicaHelena said:
@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)?
 

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  • #12
@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?
 
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  • #13
JessicaHelena said:
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).

JessicaHelena said:
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?
 

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Related to The direction of induced current and magnetic field produced

What is the relationship between the direction of induced current and the magnetic field produced?

The direction of the induced current is always perpendicular to the direction of the magnetic field. This is known as Lenz's law, which states that the induced current will flow in a direction that opposes the change in magnetic flux.

How can the direction of induced current be determined?

The direction of induced current can be determined using the right hand rule. If you point your right thumb in the direction of the magnetic field and curl your fingers, the direction your fingers point in is the direction of the induced current.

What factors affect the direction of induced current?

The direction of induced current is affected by the strength of the magnetic field, the speed at which the magnetic field changes, and the angle between the magnetic field and the conductor.

Can the direction of induced current be reversed?

Yes, the direction of induced current can be reversed by changing the direction of the magnetic field or by changing the direction of the motion of the conductor.

How does the direction of the magnetic field produced by induced current differ from the direction of the magnetic field that caused it?

The direction of the magnetic field produced by induced current is always opposite to the direction of the magnetic field that caused it. This is because the induced current creates its own magnetic field that opposes the change in the original magnetic field.

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