The earth\'s magnetic field, with a magnetic dipole moment of 8.0 x 1022 Am2, is

Question

The earth's magnetic field, with a magnetic dipole moment of 8.0 x 1022 Am2, is generated by currents within the molten iron of the earth's outer core. Suppose we model the core current as a 3000- km-diameter current loop made from a 1000-km-diameter"wire. The loop diameter is measured from the centers of this very fat wire. Part A What is the current in the current loop? Express your answer to two significant figures and include the appropriate units. 1= 1 Value IA Submit Request Answer Part B What is the current density J in the current loop? Express your answer to two significant figures and include the appropriate units. Value A/m Submit Request Answer

Explanation / Answer

radius of loop R = 3000/2 = 1500 km = 15*10^5 m

radius of the wire r = 1000/2 = 500 km = 5*10^5 m

part(A)

magnetic dipole moment = I*A1

A1 = area of the loop = pi*R^2

current in wire = dipole moment/A1 = 8*10^22/(pi*(15*10^5)^2) = 1.13*10^10 A

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part B

current density J = I/A2

A2 = area of corss section = pi*r^2

J = 1.13*10^10 /(pi*(5*10^5)^2)

J = 1.4*10^-2 A/m^2

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Jwire = Iwire/Awire

A wire = pi*Rwire^2 = pi*(0.7*10^-3)^2

Jwire = 3/(pi*(0.7*10^-3)^2) = 19.5*10^5 A/m^2

Jloop/Jwire = 1.4*10^-2/(19.5*10^5) = 7.2*10^-9

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