Two parallel wires carrying currents in the same direction.

[David Truong]

Homework Statement

Two parallel wires both carry currents directed from left to right. A circular wire loop lies in the plane of the two wires midway between them. The currents are positive charges. Sketch the changes in the magnetic fields induced and the resultant current direction in the loop when:

a) I1 is increasing and I2 is constant
b) I1 is decreasing at a constant rate and I2 is decreasing at twice that rate

The diagram essentially looks like this:

-------------------------> I1
o
-------------------------> I2

Homework Equations

a) Right Hand Rule
b) Electromagnetic Induction: 1) a changing magnetic field produces an emf, and 2) a current produced by an induced emf moves in a direction so that its magnetic field opposes the original change in flux.

The Attempt at a Solution

Since the two parallel wires both carry currents in the same direction, they attract each other. Using the right hand rule, with the thumb in the direction of the current, both magnetic fields produced by the wires are moving counterclockwise.

For a) I am assuming since I1 is increasing, the changing magnetic field it produces will induced an emf/current in the circular loop, but I2 will not produce a current in the loop because its current is constant and, subsequently, its magnetic field is constant. The resultant current direction in the loop will be, I am assuming, counterclockwise, based on #2 of the electromagnetic statements above.

My problem is I do not know how to draw this.

For b) Since both currents, I1 and I2, are decreasing, they both produce an induced emf in the circular loop. My question is if they are both decreasing, can we assuming that the current has changed direction (i.e. rather than left to right, that it is moving from right to left?).

In any case, I1 will induce an emf in the circular loop as before, with the direction of the produced magnetic field opposing the original change in magnetic flux from the straight wire. That is, the induced current will be counterclockwise, and the magnetic field in the wire clockwise. I2 will produce the same effects as I1; however, I do not know how the differing rate of decrease in the two wires will affect resultant current and magnetic fields.

This was a shot in the dark. I am not sure whether this is correct or even how to draw this on a diagram. Any help and/or feedback is appreciated!

 

[Merlin3189]

(a) Are you familiar with the arrow symbol for showing magnetic field (or other vector) perpendicular to the paper?
Use + in a circle for an arrow going away (tail feathers), use a dot in a circle for an approaching arrow (point)
I don't know how you can show change on a diagram. Perhaps just label the vector and write that it is increasing or decreasing?
BTW I found your first counterclockwise ambiguous. It depends which way you are looking. But I think you have it correct for (a).
============
(b)

...both currents, I1 and I2, are decreasing, they both produce an induced emf in the circular loop. My question is if they are both decreasing, can we assuming that the current has changed direction

Why do you want to assume this?
What if we do? Is it now decreasing or increasing in magnitude?
What if we don't?

Maybe you are thinking that a current going in one direction and increasing in magnitude will always be going in the same direction, but a current that is decreasing in magnitude might eventually get to zero and then ...?
Perhaps you should think about this second situation just during the time before the current reaches zero. (If it ever does. Remember Zeno's paradox)
And then see what happens if it did change direction. You may get a pleasant surprise.

I do not know how the differing rate of decrease in the two wires will affect resultant current and magnetic fields.

How does the magnitude of a current affect the magnetic field it produces?
How does a magnetic field induce a current - what properties of the field affect the induced current?

 

[haruspex]

both magnetic fields produced by the wires are moving counterclockwise

That depends whether you are looking from the left of the picture or from the right. I would have thought that looking from the left they'd be clockwise.

The resultant current direction in the loop will be, I am assuming, counterclockwise

Think in terms of the changing (net) flux. Will increasing the I1 current increase the net flux into the page or out of the page? Which direction of current in the loop will oppose that change?

I do not know how to draw this.

You could try representing flux lines with two different symbols, showing the density change.

if they are both decreasing, can we assuming that the current has changed direction

No, why? It could just be the current is in the same direction but weaker.

I do not know how the differing rate of decrease in the two wires will affect resultant current

Again, consider net change in flux. The loop doesn't 'know' where these flux lines come from, and only feels the net flux.