B field btwn two current carrying wires

[sonya]

I just had a quick thing i wanted to clarify...

The question was:
If u have two horizontal parallel current carrying wires 196 cm apart, with the bottom wire carrying a current of 2.2 A to the west and the top 1.1 A to the west, what is the magnetic field at the point P? Point P being the midpoint between the 2 wires.

What I thot you would do is just find the 2 separate B-fields due to each wire and then add them. However, the answer in the book says that it is just the field due to bottom wire. I was wondering why this is and how come otherwise we add the fields, or subtract depending on the current direction.

 

[Doc Al]

What I thot you would do is just find the 2 separate B-fields due to each wire and then add them. However, the answer in the book says that it is just the field due to bottom wire. I was wondering why this is and how come otherwise we add the fields, or subtract depending on the current direction.

Yes, you add the separate B-fields.

The B-field is a vector. (Use the right hand rule to find the direction of the field.) The field from the top wire (carrying 1.1 A) is directed opposite to the field from the bottom wire (carrying 2.2 A). (Assuming one wire is directly beneath the other.)

I don't see how the book's answer can be right.

 

[M98Ranger]

It is correct that in this scenario, the magnetic field at point P would only be due to the bottom wire. This is because the magnetic fields from the two wires cancel each other out at this point.

To understand this, we need to look at the direction of the magnetic fields from each wire. The magnetic field around a current-carrying wire is in the form of concentric circles, with the direction of the field being determined by the direction of the current. In this case, both wires are carrying current in the same direction (to the west), so the direction of the magnetic fields around each wire would also be the same.

At point P, the magnetic fields from each wire are pointing in opposite directions and are of equal strength. This results in the two fields canceling each other out, leaving only the field from the bottom wire.

In other scenarios, where the currents are flowing in opposite directions, the magnetic fields from each wire would add together. This is because the fields would be pointing in the same direction, resulting in a stronger combined field at that point.

It is important to note that when adding or subtracting magnetic fields from different sources, we must take into account the direction of the fields as well as their strengths. In this case, the direction of the fields from the two wires is what determines whether they add or cancel each other out.

I hope this clarifies your doubt. Keep up the good work in understanding magnetic fields!