Consider two straight conductors of length 0.9m, carrying current of 19.9A and 12A respectively. If they are placed 0.3m apart, what is the value 10^6 ×F, where F is the magnitude of the force (in N) between these two conductors. Express the answer with one decimal place.
To calculate the force between two straight conductors carrying current, we can use Ampere's law. Ampere's law states that the force per unit length between two parallel conductors is directly proportional to the current in each conductor and inversely proportional to the distance between them.
The formula to calculate the force (F) between two conductors is given by:
F = (μ₀ × I₁ × I₂ × L) / (2π × d)
Where:
F: Force between the conductors
μ₀: Permeability of free space = 4π × 10^(-7) N/A²
I₁: Current in the first conductor
I₂: Current in the second conductor
L: Length of either conductor
d: Distance between the conductors
Given:
I₁ = 19.9A
I₂ = 12A
L = 0.9m
d = 0.3m
Substituting the given values into the formula, we have:
F = (4π × 10^(-7) N/A² × 19.9A × 12A × 0.9m) / (2π × 0.3m)
Simplifying the equation:
F = (4π × 10^(-7) × 19.9 × 12 × 0.9) / 0.6
F = 9.545 × 10^(-6) N
To express the answer with one decimal place, we multiply the magnitude of the force by 10^6:
10^6 × 9.545 × 10^(-6) N
= 9.545 N
Therefore, the value of 10^6 × F, where F is the magnitude of the force, is 9.5.