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A long straight wire (radius 3.0 mm) carries a constant current distributed uniformly over a cross section perpendicular to the axis of the wire. If the current density is 100 A/m2 The magnitudes of the magnetic field at (a) 2.0 mm from the axis of the wire and (b) 4.0 mm from the axis of the wire ls

A long straight wire (radius 3.0 mm) carries a constant current distributed uniformly over a cross section perpendicular to the axis of the wire. If the current density is 100 A/m2 The magnitudes of the magnetic field at (a) 2.0 mm from the axis of the wire and (b) 4.0 mm from the axis of the wire ls

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Grade:12th pass

1 Answers

Arun
25763 Points
3 years ago
By Ampere's law, ∫ B ▪ dL = (µo)I, where I is the enclosed current. 

a) 
I = JA 
I = J(πr²) 

∫ B ▪ dL = (µo)I 
B(2πr) = (µo)(J)(πr²) 
B = (µo)(J)(r) / 2 

B = (1.257e-6 N/A²)(100 A/m²)(2e-3 m) / 2 
B = 1.3e-7 T 

b) 
I = JA 
I = J(πR²) 

∫ B ▪ dL = (µo)I 
B(2πr) = (µo)(J)(πR²) 
B = (µo)(J)(R²) / (2r) 

B = (1.257e-6 N/A²)(100 A/m²)(3e-3 m)² / (2 * 4e-3 m) 
B = 1.4e-7 T

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