B-Field at a Perpendicular Distance

In summary, we have two long parallel wires with a distance of 28.28 cm between them, both carrying a current of 2.2 A in the same direction (south). We are asked to find the B-field at a point that is 23 cm away from both wires. Using the equation B=(u0*I)/(2Pi*r), we can calculate the B-field to be 3.84uT. However, this calculation is incorrect as it does not take into account the 3D aspect of the problem. Instead, we must visualize the currents as coming straight out of the page and use vector addition to find the final B-field at point P.
  • #1
chunkytuna21
37
0
Two long horizontal straight parallel wires are 28.28 cm apart and each carries a current of 2.2 A in the same direction, namely, due south. What is the B-field at a point that is a perpendicular distance of 23 cm from both wires? Answer in microtesla.

B= (u0*I)/(2Pi*r)
u0= 4Pi*10^-7= 1.26*10^-6

23cm= 0.23m
2.2A*2= 4.4A
B= (1.26*10^-6)(4.4)/(2Pi*0.23)= 3.84*10^-6T= 3.84uT

3.84uT is incorrect. I don't really know what to do here. I'm pretty sure I have the right equation, but the fact that it's two wires throws me off. Do I add the currents or subtract them? Does the 28.28cm come into play? Is my conversion from tesla to microtesla correct?
Where am I going wrong? Any help would be greatly appreciated.
 
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  • #2
I think you are missing the 3D aspect of this. Draw two dots to represent the currents coming straight at you out of the page. Mark the distance between them 28.28 cm. Now, where is your point where you are calculating the field? Must be a little above or below the halfway point between the currents, right? Sketch arrows to show the direction of the field due to each current at that point. You'll see that you have a vector addition calculation to do in order to get the final answer.
 
  • #3
I didn't understand that at all. So I should draw something like this? And then the point is 23cm from the middle?

________________________<2.2A South______________

28.28cm

________________________<2.2A South______________
 
  • #4
wires.jpg

Find the magnetic field vectors at P due to A and B. Add them.
 

FAQ: B-Field at a Perpendicular Distance

What is the B-field at a perpendicular distance?

The B-field at a perpendicular distance is the magnetic field strength at a specific distance away from a magnetic source, measured at a 90 degree angle from the source.

How is the B-field affected by distance?

The B-field decreases as the distance from the source increases. This is because the magnetic field lines spread out and become weaker as they move away from the source.

What is the equation for calculating the B-field at a perpendicular distance?

The equation is B = μ₀I/2πr, where B is the magnetic field strength, μ₀ is the permeability of free space, I is the current, and r is the distance from the source.

What units are used to measure the B-field at a perpendicular distance?

The B-field is typically measured in units of tesla (T) or gauss (G).

What factors can affect the B-field at a perpendicular distance?

The B-field can be affected by the strength of the current, the distance from the source, the permeability of the material surrounding the source, and the orientation of the source and the measuring point.

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