The edge length of the square is 5.2 meters.
The magnetic field of a square loop is given by:
B = (μ₀/2π) * (I * a)/(a² + d²)^(1/2)
where:
μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A)
I is the current (43 A)
a is the side length of the square loop (m)
d is the distance from the center of the loop (42 cm = 0.42 m)
We are given that B = 7.0 nT = 7.0 × 10⁻⁹ T. We can solve for a as follows:
a = (μ₀I / (2πB)) * √(a² + d²)
Substituting in the given values, we get:
a = (4π × 10⁻⁷ T·m/A * 43 A / (2π * 7.0 × 10⁻⁹ T)) * √(a² + (0.42 m)²)
Simplifying, we get:
a = 24.8 * √(a² + 0.1764 m²)
Squaring both sides, we get:
a² = 615.04 + 24.8a² + 0.043264
Combining like terms, we get:
22.8a² = 615.0864
Dividing both sides by 22.8, we get:
a² = 27.021
Taking the square root of both sides, we get:
a = 5.19 m
Rounding to two significant figures, we get:
a ≈ 5.2 m
Therefore, the edge length of the square is 5.2 meters.