Final answer:
To calculate the value of the resistor R, we can use the equation for force between two parallel wires. By equating the calculated force per unit length with the given force per unit length, we can solve for R. The value of resistor R in this case is 100 Ω.
Step-by-step explanation:
To calculate the force between two parallel wires, we can use the equation:
force per unit length = (μ₀ × current₁ × current₂)/(2π × distance)
Given that the wires are 10 cm long and separated by 5.0 mm, we have:
force per unit length = (4π × 10⁻⁷ T · m/A) × (5 × 10⁻³ A) × (5 × 10⁻² m) / (2π × 0.005 m)
Simplifying the expression, we get:
force per unit length = 125 × 10⁻⁷ N/m
Since the force between the wires is given as 1.26 × 10⁻⁴ N, we can set up an equation:
force per unit length = (1.26 × 10⁻⁴ N) / (10 cm)
Solving for force per unit length, we find:
force per unit length = 12.6 × 10⁻⁶ N/m
Equating the two expressions for force per unit length, we get:
(125 × 10⁻⁷ N/m) = (12.6 × 10⁻⁶ N/m)
Algebraically solving for the unknown resistor, R:
R = (12.6 × 10⁻⁶ N/m) / (125 × 10⁻⁷ N/m)
R = 100 Ω