To determine the force per unit length between two parallel wires carrying current, we can use Ampère's force law. This law states that two parallel wires carrying current will exert a force on each other, and the nature of this force—whether attractive or repulsive—depends on the direction of the currents flowing through the wires. Let's break this down step by step.
Understanding the Basics
When two wires carry electric current, they create magnetic fields around themselves. The direction of the magnetic field produced by each wire can be determined using the right-hand rule: if you point your thumb in the direction of the current, your fingers curl in the direction of the magnetic field.
Calculating the Force
The formula to calculate the force per unit length (F/L) between two parallel wires is given by:
- F/L = (μ₀ * I₁ * I₂) / (2π * d)
Where:
- F = force between the wires
- L = length of the wires
- μ₀ = permeability of free space (approximately 4π x 10-7 T·m/A)
- I₁ and I₂ = currents in the wires (in Amperes)
- d = distance between the wires (in meters)
Plugging in the Values
In your case:
- I₁ = I₂ = 300 A
- d = 1.5 cm = 0.015 m
Now, substituting these values into the formula:
- F/L = (4π x 10-7 T·m/A * 300 A * 300 A) / (2π * 0.015 m)
We can simplify this:
- F/L = (4 x 10-7 * 300 * 300) / (2 * 0.015)
- F/L = (4 x 10-7 * 90000) / (0.03)
- F/L = (3.6 x 10-2) / (0.03)
- F/L = 1.2 N/m
Nature of the Force
Now, regarding whether the force is attractive or repulsive: if the currents in both wires flow in the same direction, the force between them is attractive. Conversely, if the currents flow in opposite directions, the force is repulsive. In your scenario, since both wires are carrying a current of 300 A in the same direction, the force is attractive.
Summary
To summarize, the force per unit length between the two wires is 1.2 N/m, and since the currents are in the same direction, the force is attractive. Understanding the relationship between current direction and the resulting force helps clarify many concepts in electromagnetism.
