Anti Parallel Currents and Magnetic Field

[GingerBread27]

Two long parallel wires are a distance of d = 4.5 cm apart and carry equal antiparallel currents of 1 Amperes. Find the magnetic field intensity (in T) at the point P which is equidistant from the wires. (R = 2 cm).


Now I really thought I had this. I thought the magnetic field at P would be the superposition of the vectors of the magnetic fields from each of the two wires. After working with the equations I figured out the net magnetic field was in the positive x directions with magnitude B=(2kId)/(x^2), where k=(Mo/4pi), I=1 A, d=4.5cm, and x=2cm. I get the wrong answer. Why?

 

[Gamma]

check the value of x.

x = 3 cm.


$$x=\sqrt(R^2 + (d/2)^2)$$

 

[wais]

It is important to note that in this scenario, the two wires are carrying equal but antiparallel currents. This means that the direction of the magnetic field created by one wire will be in the opposite direction of the magnetic field created by the other wire. Therefore, when calculating the net magnetic field at point P, the two vectors should be subtracted, not added. This results in a net magnetic field of zero at point P.

To understand this concept better, imagine the wires as two arrows pointing in opposite directions. When you add them together, they cancel each other out and you end up with no net direction. This is the same principle with antiparallel currents and magnetic fields.

Another way to look at it is through the right-hand rule. If you use your right hand to point your fingers in the direction of the current in one wire, and then curl your fingers towards the direction of the current in the other wire, your thumb will point in the opposite direction, indicating the net magnetic field at point P is zero.

In conclusion, when dealing with antiparallel currents and magnetic fields, it is important to remember to subtract the two vectors instead of adding them together. This will result in the correct calculation of the net magnetic field at any given point.