Faradays Law - Induced Current

[rowkem]

Homework Statement

A loop of wire is situation between a wire (Wire 1) that is perpendicular to the loop and another wire (Wire 2) that is parallel to the loop (the diagram has the loop and Wire 2 in the plane of the page, Wire 1 is running "through" the page). Is a current induced, and in what direction, in the wire loop if the following occur:

1) Steady flow of current in wire 1.
2) Increasing flow of current in wire 1 into the page.
3) Steady flow of current in wire 2 toward the top of the page.
4) Increasing flow of current in wire 2 towards the bottom of the page.
5) Increasing flow of current in wire 1 out of the page and a decreasing flow of current in wire 2 towards the top of the page.
6) Steady flow of current in wire 2 towards the top of the page, and wire 2 is also being moved away from the loop

Homework Equations

Right hand rule? Faradays Law?

The Attempt at a Solution

1) No induced current since the field produced by wire 1 is not changing
2) Current is induced but, I've no clue how to work the right hand rule and whatnot to tell me which direction
3) Same as 1
4) Same as 2
5) They both induce some current since the field is changing but, again, I don't know how the combination of both would affect the direction and net magnitude
6) Current is induced since B is changing; again, no clue on direction.

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So, I understand that a current is induced whenever the field around the loop changes. That occurs in 2, 4, 5?, and 6. However, the issue I'm having is determining which direction the induced current in the loop is flowing (cw or ccw); especially with #5. Any help would be greatly appreciated. Thanks.

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Upon some research, I've reworked my answers. If these could be checked:

1,2,3: No current is induced
4,5,6: Current is induced, all 3 in the ccw direction.

Thanks!

 

[anathema]

Hello,

You are correct in your understanding that a current is induced in the loop whenever the magnetic field changes. To determine the direction of the induced current, you can use the right hand rule for electromagnetic induction. This rule states that if you point your thumb in the direction of the magnetic field, and your fingers in the direction of the motion of the conductor, your palm will face the direction of the induced current.

Now, let's look at each scenario:

1) Since the field produced by wire 1 is not changing, there is no induced current in the loop.

2) In this scenario, the field produced by wire 1 is increasing into the page. If we use the right hand rule, we can see that the induced current in the loop will flow in a counterclockwise direction. This is because the field is increasing into the page, and the motion of the conductor (wire 1) is also into the page.

3) Similar to scenario 1, there is no induced current in the loop because the field produced by wire 2 is not changing.

4) In this case, the field produced by wire 2 is increasing towards the bottom of the page. Using the right hand rule, we can see that the induced current in the loop will flow in a counterclockwise direction. This is because the field is increasing towards the bottom of the page, and the motion of the conductor (wire 2) is also towards the bottom of the page.

5) This scenario is a bit more complex, but using the right hand rule, we can determine the direction of the induced current. The key here is to consider the net field produced by both wires. Wire 1 is now producing a field out of the page, while wire 2 is producing a field towards the top of the page. The net field will be a combination of these two fields. Using the right hand rule, we can see that the induced current in the loop will flow in a counterclockwise direction. This is because the net field is out of the page, and the motion of the conductor (wire 1) is also out of the page.

6) In this scenario, the field produced by wire 2 is not changing, but the wire is being moved away from the loop. This motion creates a changing magnetic field, which induces a current in the loop. Using the right hand rule, we can see that the induced current in the loop will flow

 

[nlightner]

Your answers for 1-3 are correct, as the steady flow of current in wire 1 or wire 2 does not cause any changes in the magnetic field around the loop.

For 4, the induced current in the loop would flow in a counter-clockwise direction, as the increasing flow of current in wire 2 towards the bottom of the page would create a magnetic field that is directed into the page, which would induce a current in the loop that opposes this change in the magnetic field.

For 5, the induced current in the loop would also flow in a counter-clockwise direction, as the increasing flow of current in wire 1 out of the page would create a magnetic field that is directed out of the page, and the decreasing flow of current in wire 2 towards the top of the page would create a magnetic field that is directed into the page. These two fields would oppose each other, causing a net change in the magnetic field that would induce a current in the loop in the counter-clockwise direction.

For 6, the induced current in the loop would flow in a clockwise direction, as the steady flow of current in wire 2 towards the top of the page would create a magnetic field that is directed into the page, and moving wire 2 away from the loop would decrease this magnetic field, causing a change that would induce a current in the loop in the clockwise direction to oppose this change.

Overall, your understanding of Faraday's Law is correct, and the right hand rule can be used to determine the direction of the induced current in these situations. Keep in mind that the direction of the induced current will always be such that it opposes the change in the magnetic field that caused it.