Question

The two 10-cm-long parallel wires in the figure are separated by 5.0 mm. For what value of the resistor r will the force between the two wires be 1.26×10−4 n?

Answer 1

if you read the question you will see that some requirements are missing. by Googling the question, the complete content could be found here:

https://www.chegg.com/homework-help/questions-and-answers/two-10-cm-long-parallel-wires-figure-separated-50--value-resistor-force-two-wires-11-10-4-q1288728

Answer:

1.3 ohm

Explanation:

length of first wires (L) = 10 cm = 0.1 m

distance of the wires apart (d) = 5 mm = 0.005 m

force between the two wires (f) = 1.26 x 10^{-4} N

force between parallel carrying conductors = $\frac{μ.I1.I2.L}{2π.d}$

where

• I1 is the current in the first wire

        I1 = V1/R1 = 9/2 = 4.5 A

• I2 is the current in the second wire
• μ is = 4π x 10^{-7} T.m/A
• d is the distance of the wires apart
• L is the length of the wires

$1.26 x 10^{-4} = \frac{4π x 10^{-7} x 4.5 x 0.10 x I2}{2π x 0.005}$

I2 = $\frac{ 2π x 0.005 }{ 4π x 10^{-7} x 4.5 x 0.10 }$

I2 = 7A

now we can finally get the resistance from ohms law, V = I x R

R2 = V2/I2 = 9/7 = 1.3 ohm