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## 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!