Final answer:
To create Earth's magnetic dipole moment of 8.00 × 10²² J/T, a current of approximately 2.06 × 10¶ A flowing around a circular path of radius 3500 km would be required.
Step-by-step explanation:
To determine the amount of current needed to create a magnetic dipole moment of 8.00 × 10²² J/T, we must use the formula for the magnetic dipole moment (μ) of a current loop, which is given by μ = I×A, where I is the current and A is the area of the loop. For a circular loop, the area A is πr², where r is the radius of the loop.
In this case, since the Earth's magnetic dipole moment is 8.00 × 10²² J/T and the radius provided is 3500 km, which we convert to meters (3500 × 10³ m), we can set up the equation 8.00 × 10²² J/T = I × π × (3500 × 10³ m) ². Solving for I, we find:
I = μ / (πr²) = 8.00 × 10²² J/T / [π × (3500 × 10³ m)²] ≈ 2.06 × 10¶ A
Therefore, a current of approximately 2.06 × 10¶ A flowing around a circular path of radius 3500 km would be needed to create a magnetic dipole of the given magnitude.