When the current through a circular loop is 6.0 A, the magnetic field at its center is 2.0 x 10 T. What is the radius of the loop?
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We can use Ampere's law to solve this problem. Ampere's law states that the magnetic field generated by a current-carrying wire is directly proportional to the current and inversely proportional to the distance from the wire.
The equation for the magnetic field at the center of a circular loop is given by:
B = (μ₀ * I) / (2 * R)
Where B is the magnetic field at the center of the loop, μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A), I is the current through the loop, and R is the radius of the loop.
Plugging in the known values:
2.0 × 10⁻⁷ T = (4π × 10⁻⁷ T·m/A * 6.0 A) / (2 * R)
Simplifying the equation:
2.0 × 10⁻⁷ T = (2π × 10⁻⁷ T·m/A) / R
Cross multiplying:
4π × 10⁻⁷ T·m/A * R = 2π × 10⁻⁷ T
Simplifying:
R = 0.5 m = 50 cm
Therefore, the radius of the loop is 50 cm.
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