Shown at right is a cross-sectional view of two long straight wires that are parallel to one another. One wire carries a current i1, out of the page; the other carries an equal current i2, into the page.
The correct answer and explanation is :
To analyze the magnetic field produced by two long, straight, parallel wires carrying equal but opposite currents, let’s apply Ampère’s Law and the right-hand rule.
Correct Answer:
The magnetic fields produced by the two wires interact in a specific way:
- Between the wires: The fields from both wires add up, resulting in a stronger magnetic field.
- Outside the wires: The fields from each wire cancel out at symmetrical points, leading to a weaker or zero net field at far distances.
Since ( I_1 ) is out of the page (represented by a dot: ⊙) and ( I_2 ) is into the page (represented by a cross: ⊗), we use the right-hand rule to determine the direction of the magnetic fields:
- For ( I_1 ) (out of the page): The magnetic field circles counterclockwise.
- For ( I_2 ) (into the page): The magnetic field circles clockwise.
At a point between the wires, the fields are in the same direction and reinforce each other.
At a point outside the wires, the fields are opposite and tend to cancel each other out.
Explanation:
Using the Biot-Savart Law or Ampère’s Law:
[
B = \frac{\mu_0 I}{2\pi r}
]
where ( B ) is the magnetic field, ( \mu_0 ) is the permeability of free space, ( I ) is the current, and ( r ) is the distance from the wire.
Since the wires carry equal currents but in opposite directions, the force between them follows Ampère’s force law:
- If currents flow in the same direction, they attract.
- If currents flow in opposite directions, they repel.
Thus, these two wires repel each other due to their opposite currents.
Here is an image illustrating the cross-sectional view of two parallel wires with opposite currents. The magnetic field lines are depicted circling the wires, reinforcing each other between the wires and partially canceling outside. This results in a repelling force between the wires.