Final answer:
The current in the other wire is 1.26 × 10³ A.
Step-by-step explanation:
To find the current in the other wire, we can use the formula for the force per unit length between two parallel wires:
F = (μ₀ * I₁ * I₂ * d) / (2π * r)
Where:
- F is the force per unit length
- μ₀ is the magnetic constant (4π × 10⁻⁷ N/A²)
- I₁ is the current in one wire (4.60 A)
- I₂ is the unknown current in the other wire
- d is the separation between the wires (3.70 cm or 0.037 m)
- r is the distance from one wire to the other (0.037 m)
Plugging in the values, we get:
F = (4π × 10⁻⁷ N/A² * 4.60 A * I₂ * 0.037 m) / (2π * 0.037 m)
Simplifying the equation:
_F = (4π × 10⁻⁷ N/A² * 4.60 A * I₂)/2_
Now, we can solve for I₂ by rearranging the formula:
_I₂ = (2 * F)/ (4π × 10⁻⁷ N/A² * 4.60 A)
Calculating I₂ gives us:
I₂ = (2 * 2.30 × 10⁻⁴ N/m) / (4π × 10⁻⁷ N/A² * 4.60 A)
I₂ = 1.26 × 10³ A
Therefore, the current in the other wire is 1.26 × 10³ A.