The magnitude of the magnetic field 50 cm from a long, thin, straight wire is 8.0 μT. What is the current through the long wire?
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To find the current through the long wire, we can use Ampere's Law. According to Ampere's Law, the magnetic field around a long, straight wire is given by:
B = (μ₀ * I) / (2π * r)
where B is the magnetic field, μ₀ is the permeability of free space (4π × 10^(-7) T·m/A), I is the current through the wire, and r is the distance from the wire.
We can rearrange this equation to solve for the current I:
I = (B * 2π * r) / μ₀
Plugging in the given values:
B = 8.0 μT = 8.0 × 10^(-6) T
r = 50 cm = 0.50 m
μ₀ = 4π × 10^(-7) T·m/A
Substituting these values into the equation, we get:
I = (8.0 × 10^(-6) T * 2π * 0.50 m) / (4π × 10^(-7) T·m/A)
= (8.0 × 10^(-6) T * π * 0.50 m) / (2π × 10^(-7) T·m/A)
= (4.0 × 10^(-6) T·m) / (2 × 10^(-7) T·m/A)
= 20 A
Therefore, the current through the long wire is 20 A.
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