Ten amps flow through a square loop where each side is 20 cm in length. At each corner of the loop is a 0.01-cm segment that connects the longer wires as shown. Calculate the magnitude of the magnetic field at the center of the loop.
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To calculate the magnitude of the magnetic field at the center of the loop, we can use the formula for the magnetic field created by a current-carrying loop at its center:
B = (μ₀ * I * N) / (2 * R)
where B is the magnetic field, μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A), I is the current flowing through the loop, N is the number of turns in the loop, and R is the radius of the loop.
In this case, the current flowing through the loop is 10 A, there is only one turn in the loop, and the radius of the loop is half the length of one side of the square, so R = 10 cm.
Plugging these values into the formula:
B = (4π × 10⁻⁷ T·m/A * 10 A * 1) / (2 * 10 cm)
B = (4π × 10⁻⁷ T·m) / (20 cm)
B = 2π × 10⁻⁸ T·m
Therefore, the magnitude of the magnetic field at the center of the loop is 2π × 10⁻⁸ T·m.
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