Why Does the Force Calculation on Parallel Wires Yield Zero?

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SUMMARY

The discussion centers on the calculation of the force per unit length between two parallel wires carrying currents of 40.0 A, spaced 20.0 cm apart. The user initially calculated the magnetic field using the formula B = (4 × 10^-7 T·m/A) × I / (2πR) and obtained a value of 0.000013 T. However, the user incorrectly applied the force formula F/L = IBsin(θ) by assuming sin(θ) to be zero, leading to confusion in the results. The correct approach requires recognizing that the angle θ is 0 degrees when currents are in the same direction, resulting in a force per unit length that is not zero.

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  • Familiarity with the Biot-Savart Law
  • Knowledge of magnetic fields generated by current-carrying wires
  • Basic trigonometry, particularly sine functions
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  • Explore the concept of magnetic force between parallel wires in different current directions
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myersb05
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I felt like this problem was simple. We submit our answers in WebAssign however, and I can not find the correct solution.

Two parallel wires are 20.0 cm apart, and each carries a current of 40.0 A.

(a) If the currents are in the same direction, find the force per unit length exerted on one of the wires by the other.

(b) Repeat the problem with the currents in opposite directions.


I know that Bwire=4*10^-7(constant)*I/2piR
So I calculated Bwire by using 4*10^-7*40/2pi*.2 and got a value of .000013 for each of the wires because their distances apart and currents are equal.

I also know that F/L=IBsin(theta). I plugged my current of 40 amps and my newly calculated B wire in. I thought that there is no angle between two parallel wires so using 0, my values for force came out as 0. After finding that was not correct, I disregarded the sin part of the equation thinking that it would probably be 1 or -1. I came up with a F/L value of .00052 N/m which is not correct. Where am I going wrong?
 
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Hi myersb05,

myersb05 said:
I felt like this problem was simple. We submit our answers in WebAssign however, and I can not find the correct solution.

Two parallel wires are 20.0 cm apart, and each carries a current of 40.0 A.

(a) If the currents are in the same direction, find the force per unit length exerted on one of the wires by the other.

(b) Repeat the problem with the currents in opposite directions.


I know that Bwire=4*10^-7(constant)*I/2piR
So I calculated Bwire by using 4*10^-7*40/2pi*.2 and got a value of .000013 for each of the wires because their distances apart and currents are equal.

I don't believe this formula is quite right. Do you see what's missing?
 

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