Magnetic Field Between Two Wires

AI Thread Summary
Two long parallel wires, spaced 20 cm apart, carry currents of 5.0 A and 8.0 A in the same direction, raising the question of whether a point exists between them where the magnetic field is zero. To find this point, the magnetic field equations for each wire must be set equal, but the distance from each wire to the point must be expressed differently, as they are not equidistant unless at the midpoint. The correct approach involves defining one distance as r and the other as 20 cm - r. By substituting the known values into the equations, a solvable equation for r can be derived. This method effectively determines the location of the zero magnetic field point between the two wires.
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Homework Statement


Two long parallel wires 20 cm apart carry currents of 5.0 A and 8.0 A in the same direction. Is there any point between the two wires where the magnetic field is zero.


Homework Equations


B=muI1I2/(2pir)


The Attempt at a Solution


I set the two B equations equal to each other to solve for r, but am stuck on what to do once I set them equal to each other: B1=B2, muI1/2pir = muI2/2pir
 
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I set the two B equations equal to each other to solve for r, but am stuck on what to do once I set them equal to each other: B1=B2, muI1/2pir = muI2/2pir
The trouble with that a point that is r from one wire is not going to be r from the other wire, unless the point is exactly half way between them. You pretty much need to express one of them as r and the other as .20 - r. This limits you to the plane of the two wires, but I think that is the unstated intent of the question. Anyway, you can now put in your known numbers and you'll have a nice equation with only the unknown r to solve for. Go for it!
 

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