Two parallel wires conduct equal currents in opposite directions (as is the case with ordinary household electric cords). at a point in the plane of the wires midway between them, (a) what is the direction of the combined magnetic field generated by the two currents? (b) do the individual fields of the wires cancel or reinforce each other there? (c) at a point in the plane of the wires but far away to one side, do the individual fields of the wires tend to cancel or reinforce each other? explain your answer to part c.

(a) Upward (away from the plane)

Let's assume that the wires are placed horizontal on the plane. We can determine the direction of the magnetic field produced by each wire by using the right hand rule:

- Thumb: direction of the current in the wire

- Other fingers wrapped around the thumb: direction of the magnetic field around the wire

The two wires are carrying current in opposite directions: let's assume that the wire on the right is carrying current to the north, while the wire on the left is carrying current to the south.

For the wire on the right, we have:

- thumb (current): north

- Other fingers (magnetic field): at a point midway between the wires, the direction is upward (away from the plane)

For the wire on the left, we have:

- thumb (current): south

- Other fingers (magnetic field): at a point midway between the wires, the direction is upward (away from the plane) again

So, the direction of the combined magnetic field generated by the two currents is upward (away from the plane)

(b) They reinforce each other

As we described in part (a), at a point midway between the two wires the two magnetic fields are in the same direction: this means that they add together, so they reinforce each other.

(c) Cancel each other

Let's determine for example the direction of the two magnetic fields at a point on the right of the wire on the right. We have:

For the wire on the right, we have:

- thumb (current): north

- Other fingers (magnetic field): at a point on the right of the wire, the direction is downward (inside the plane)

For the wire on the left, we have:

- thumb (current): south

- Other fingers (magnetic field): at a point  on the right of the wire, the direction is upward (away from the plane) again

So, we see that the two magnetic fields have opposite directions, so they tend to cancel each other.

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