To understand the magnetic field created by two straight conductors carrying equal currents and placed perpendicular to each other, we need to delve into the principles of electromagnetism, particularly Ampère's Law and the right-hand rule. Let's break this down step by step.
Magnetic Field Around a Current-Carrying Conductor
When an electric current flows through a conductor, it generates a magnetic field around it. The direction of this magnetic field can be determined using the right-hand rule: if you point your thumb in the direction of the current, your fingers will curl in the direction of the magnetic field lines.
Analyzing the Conductors
In this scenario, we have two conductors, let's call them Conductor 1 (along AB) and Conductor 2 (along CD), both carrying equal currents in the same direction. Since they are perpendicular to each other, we can analyze the magnetic fields they produce at various points in the plane.
- Magnetic Field from Conductor 1 (AB): At any point along line CD, the magnetic field produced by Conductor 1 will be directed either into or out of the page, depending on the direction of the current.
- Magnetic Field from Conductor 2 (CD): Similarly, at any point along line AB, the magnetic field from Conductor 2 will also be directed either into or out of the page.
Finding the Intersection Point
At the intersection point of AB and CD, the magnetic fields from both conductors will interact. Since both currents are equal and the conductors are perpendicular, the magnetic fields they produce at this point will be equal in magnitude but opposite in direction. This results in a net magnetic field of zero at the intersection point.
Evaluating Other Locations
Now, let's consider points along the lines AB and CD:
- On Line AB: At any point on line AB, the magnetic field due to Conductor 2 (along CD) will still be present, while the contribution from Conductor 1 (along AB) will be zero since you are on the line of the conductor itself. Therefore, the magnetic field will not be zero along AB.
- On Line CD: Similarly, at any point on line CD, the magnetic field from Conductor 1 will be present, while the contribution from Conductor 2 will be zero. Thus, the magnetic field will not be zero along CD either.
Other Points in the Plane
For points not on either line, the magnetic fields from both conductors will combine. However, due to their perpendicular arrangement and equal current, there will be points in the plane where the magnetic fields from both conductors can cancel each other out. These points will not be limited to the intersection but can occur at specific locations based on the distances from each conductor.
Conclusion
In summary, the magnetic field is zero only at the intersection point of the two conductors. Along the lines AB and CD, the magnetic fields do not cancel out completely, and there are other locations in the plane where the fields may cancel, but they are not restricted to the lines themselves. Understanding these interactions helps in visualizing how magnetic fields behave in the presence of multiple current-carrying conductors.
