Final answer:
Using the formula derived from Biot-Savart law (μ₀I/(2r) = B), we calculate the radius of the circular loop to be approximately 0.0119 meters (11.9 millimeters) when the current is 7.5 A and the magnetic field at the loop's center is 5.0x10⁻⁴ T.
Step-by-step explanation:
When the current through a circular loop is 7.5 A, the magnetic field at its center is measured to be 5.0x10⁻⁴ T. To calculate the radius of the loop, we can use Biot-Savart law or Ampère's law for magnetism. The formula that describes the magnetic field (B) at the center of a circular loop of a single turn, due to a steady current (I), is given by
B = μ₀I/(2r)
where:
- μ₀ is the permeability of free space (4π x 10⁻⁷ T·m/A),
- I is the current through the loop,
- r is the radius of the loop.
To find the radius, we rearrange the equation to solve for r:
r = μ₀I/(2B)
Substituting the given values:
r = (4π x 10⁻⁷ T·m/A x 7.5 A) / (2 x 5.0x10⁻⁴ T)
r = (3.14 x 7.5 x 10⁻⁷ m) / (1.0x10⁻⁴)
After performing the calculation:
r ≈ 0.0119 m
Therefore, the radius of the circular loop is approximately 0.0119 meters or 11.9 millimeters.