A wire of radius R = 1.5 mm and carries a current.The current density is given by the function J = J₀ (1 - r/R)where r is measured from the center of the wire and J₀ = 1.06 * 10⁵ A/m².Use Ampère's law to find the magnetic field at the surface of the wire.What is the magnitude of B if I = 1A,R = 1.5 mm. A)148 µT B)12 µT C)100 µT D)33 µT E)37 µT

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Quizplus · Accepted Answer

The magnetic field at the surface of the wire can be found using Ampère's law: B(2πR) = μ₀I_enclosed. The current density J = J₀(1 - r/R) needs to be integrated over the cross-sectional area to find I_enclosed. Solving this gives B = μ₀I/(2πR). Substituting the given values, B ≈ 33 µT.

A Wire of Radius R = 1