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

Question

The earth's magnetic field, with a magnetic dipole moment of 8.0×1022Am2, 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

What is the current in the current loop?

What is the current density J in the current loop?

To decide whether this is a large or a small current density, compare it to the current density of a 5.0 A current in a 2.0-mm-diameter wire.

Explanation / Answer

given dipole moment of earth, m = 8*10^22 A m^2

assuming

D = 3000,000 m

d = 1000,000 m

a. current in the loop = i

i*pi*D^2/4 = m

i = 11317684842.09 A

b. current density J = 4i/pid^2 = 0.01441 A/m^2

c. for i = 5 A, d = 2 mm

J = 1591549.43 A/m^2

hecne current density of earth is very low

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