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:
Answer:
The two long, straight, parallel wires carry equal currents in opposite directions: i1i_1 out of the page and i2i_2 into the page. The magnetic fields generated by these currents interact in a predictable manner.
Using the right-hand rule for a current-carrying wire, the magnetic field around each wire forms concentric circles. For i1i_1 (out of the page), the field circulates counterclockwise, while for i2i_2 (into the page), the field circulates clockwise.
At a point directly between the two wires, the magnetic field due to both wires adds constructively if the wires are equally spaced. However, outside the wires (beyond the two), the magnetic fields oppose each other and partially cancel out.
Furthermore, the force between two parallel current-carrying wires is given by Ampère’s force law: F=μ02πi1i2dF = \frac{\mu_0}{2\pi} \frac{i_1 i_2}{d}
where dd is the separation between the wires. Since the currents are opposite, the force is repulsive. This means the two wires push away from each other.
Explanation:
- Each wire generates a magnetic field that interacts with the other.
- The right-hand rule helps determine the direction of the field.
- The net field is stronger between the wires and weaker outside.
- The two wires experience a repulsive force.
This scenario is common in electromagnetism, influencing applications such as power transmission lines, magnetic levitation, and electric motor design.
Now, I’ll generate an image illustrating the situation.
Here is the generated image illustrating the two parallel wires with opposite currents, their respective magnetic fields, and the repulsive force between them. Let me know if you need any modifications or further explanations!
