# Magnetic field Direction for conductor in a changing magnetic field.

Discussion in 'Homework Help' started by Silhorn L, Jun 27, 2017.

1. ### Silhorn L Thread Starter New Member

May 2, 2017
7
0
Hi,
So I understand the magnetic field create on a conductor opposed the applied magnetic field when that field is changing. So this makes sense:

Now, if the conductor was and magnetic field was aligned as per below picture but having conductor stationary but magnetic field changing, how would I determine the direction of induced emf?

Because the right hand rule for generators only works for force, not changing fields....

(This is not question from homework but a situation I was pondering about while studying)

2. ### MrChips Moderator

Oct 2, 2009
18,207
5,722
The Right-Hand-Rule applies to both static fields and dynamic fields.

Take an instantaneous moment of a changing field and apply the Right-Hand-Rule as if it were a constant field. The direction of the current will be as determined for that instant.

If the magnitude and direction of the field changes, then so will the magnitude and direction of the induced current.

Apr 5, 2008
19,286
3,895
Hello,

Your first 3 images do not show.
They have a strange header and show the image data. (http://data:image).
The system does not know how to handle these.

Bertus

4. ### MrAl AAC Fanatic!

Jun 17, 2014
5,752
1,220
Hi,

The emf is dependent on the CHANGE in the flux. That means that your drawing with the two magnets and one wire and field direction can not be used directly to determine the current because you need to know how the field is changing.

For example, if we apply a current to an inductor made of a wire, the field is increasing. If the current is left to right in a horizontal wire then when we reduce the drive current the field collapses and the current still flows left to right. Thus if we apply a field that is decreasing the current moves left to right. If we apply a field that is increasing, the current moves right to left. If we apply a constant static field no matter what the level of that field intensity, the current is zero.
I believe those are the actual current directions, but you could check out Lenz's Law which describes this.
It's all based on something like pPhi/pt where 'p' is the del symbol used to represent a partial derivative and Phi is the flux and t is time.

Last edited: Jun 28, 2017
5. ### Silhorn L Thread Starter New Member

May 2, 2017
7
0
The first 3 images with the cross is nothing. I tried removing them but didn't know how to.

I am getting a bit confused. So lets have a look at this picture again.

If the magnetic field for above is increasing and conductor remains stationary,I use right hand rule like so:
Index finger points in the direction of magnetic field as shown above.
Thumb points no where because there is no force
So no thumb I do not know how to orientate my hand so that my middle finger points to the current direction.

6. ### MrAl AAC Fanatic!

Jun 17, 2014
5,752
1,220
Hello again,

I think that picture may be a little misleading for this problem. That's because we see an N magnet on one side and an S magnet on the other side, and no way to really indicate how the field changes, if it really does change.
Usually for a diagram like that we see the wire being moved through the field, and then we get the generator effect. What seems to be maybe implied with this diagram is that when the N pole changes intensity at a point x,y,z somewhere out in space, the S pole changes intensity by the same amount at that same point x,y,z only with opposite polarity, thus canceling the effect of pole N. If we assume perfect symmetry (which we usually do for these academic problems) then the fields cancel at all spatial points and also their derivatives cancel if they are changing at the same rate. We also have the problem that the entire magnetic path is not shown, so we have to assume that most of the field is contained within the field between the two pole faces.

It might be easier to look at if we consider instead of two magnets, two equal and parallel wires placed where those magnets are in the drawing, with the original wire placed perfectly between the two added wires. We can then push current through the new added wires and calculate the field at the center original wire.
If the two added wire currents are the same, then the fields cancel at the center wire. If the two added wire currents increase at the same rate, then the field at the axial center of the center wire is zero, so for an infinitesimally thin filament wire the field is zero, and for a wire with finite cross section one half will produce current in one direction while the other half would produce current in the opposite direction, thus leading again to zero current in the wire. In a simpler view, the calculation would just involve the mutual inductances and the direction of the currents produced by both the left side wire and the right side wire, so it would resemble a transformer with two primaries and one secondary.
If we look at the currents going in the same direction, then we see the central field increase, and that would force current flow in the wire.
The difference with the two magnets though is that there are no field line loops enclosing the wire thus the cross product is probably zero.

Last edited: Jun 28, 2017