B field intensity of 2 parallel wires

In summary, two parallel wires with equal anti-parallel currents of 4.40 A and a center-to-center distance of 4.60 cm are given. The magnetic field intensity at point P, located at a distance of 4.00 cm from the wires, is to be found. The equation used is the magnetic field equation for a long straight wire, which is μi/2*pi*r. After attempting a solution, the user realizes that they need to account for the direction of the currents and uses the equation B = (2*μ*i*cos(theta))/(2*pi*r), where cos(theta) = R/r and r = sqrt(R^2+(d/2)^2). However, there are two errors in their
  • #1
arl146
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Homework Statement


Two long parallel wires are a center-to-center distance of 4.60 cm apart and carry equal anti-parallel currents of 4.40 A. Find the magnetic field intensity at the point P which is equidistant from the wires. (R = 4.00 cm).



Homework Equations


magnetic field for a long straight wire = μi/2*pi*r


The Attempt at a Solution


at first i thought it was just 0 T since the current is in opposite directions but that was wrong. so i worked it out and saw that the y components cancel out and you're left with the 2 x directions components. so i thought B = [itex]\frac{2*μ*i*cos(theta)}{2*pi*r}[/itex]

where cos(theta) = R/r
where r = sqrt(R2+(d/2)2)

this didnt work out for me. my answer was 7.1665340225x10^(-4) T and it said it was wrong

B= [itex]\frac{2*4*pi*10^-7*4.4*.04}{2*pi*(R^2+(d/2)^2)^(3/2)}[/itex]

anything i did wrong, plugged in wrong numbers or what?
 

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  • #2
I see two problems:

1. I don't see where the "3/2" exponent comes from in your denominator, the units do not work out properly with that exponent there.

2. It appears you made an arithmetic mistake in evaluating your expression -- I get a different number for the expression you wrote, but as I indicated I don't think the 3/2 exponent there is correct anyway.
 

1. What is the definition of "B field intensity" in the context of 2 parallel wires?

The B field intensity, also known as magnetic field intensity, is a measure of the strength of the magnetic field created by the flow of electric current through the wires. It is typically measured in units of amperes per meter (A/m).

2. How is the B field intensity affected by the distance between the parallel wires?

The B field intensity is inversely proportional to the distance between the parallel wires. This means that as the distance between the wires increases, the B field intensity decreases. This relationship follows the inverse square law.

3. What is the direction of the B field intensity between 2 parallel wires?

The direction of the B field intensity is perpendicular to the direction of the electric current flowing through the wires. This means that for two parallel wires with currents flowing in the same direction, the B field intensity will be in opposite directions between the wires, and for currents flowing in opposite directions, the B field intensity will be in the same direction between the wires.

4. How does the B field intensity change with increasing current in the parallel wires?

The B field intensity is directly proportional to the current flowing through the parallel wires. This means that as the current increases, the B field intensity will also increase. This relationship follows Ampere's law.

5. Can the B field intensity between 2 parallel wires be zero?

No, the B field intensity between 2 parallel wires cannot be zero. As long as there is a current flowing through the wires, there will be a non-zero B field intensity between them. However, the B field intensity can become very small if the currents are very small or the distance between the wires is very large.

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