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Multiple Choice
At what distance from a wire carrying a 10 Acurrent is the magnetic field strength equal to ? This is the approximate value of the earth's magnetic field.
A
B
C
D
E
F
Verified step by step guidance
1
Understand that the magnetic field (B) around a long straight wire carrying a current (I) is given by the formula: B = (μ₀ * I) / (2π * r), where μ₀ is the permeability of free space (4π x 10⁻⁷ T·m/A), I is the current, and r is the distance from the wire.
Rearrange the formula to solve for the distance (r): r = (μ₀ * I) / (2π * B).
Substitute the given values into the equation: I = 10 A and B = 50 μT (which is 50 x 10⁻⁶ T).
Calculate the expression for r using the substituted values: r = (4π x 10⁻⁷ T·m/A * 10 A) / (2π * 50 x 10⁻⁶ T).
Simplify the expression to find the distance r, ensuring units are consistent and calculations are accurate to determine the correct distance from the wire where the magnetic field strength is 50 μT.