This can be a decent approximation because the Earth's magnetic field is roughly that of a dipole.
It's easy to look-up the Radius of the earth, and we can use a rough estimate of 0.23 gauss for the horizontal component of the magnetic field at 40 degrees latitude.
A simple expression for the magnetic field due to a dipole in spherical polar coordinates is
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjt1gqqpoJWNJfrJwyDHdTUCyKTWHeDijk-sO23YnyzZBuKlQdkIcHCvMDFkHCz2_1XLXLvWrx8ecqe8BrZBMe83HChCq1JPVe2IQjtT_Cjw3nvJ-24xC3Y6MOVdi5vpDMc7h86k_mSnIE/s400/img1.png)
There's no dependence on azimuthal angle because of the symmetry axis along the dipole.
The dipole moment is then
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiFGwgFzzuq12yA56pVwOIM-Y1hpMZYnghDdA_a7e6cEEKM3tT07F9q_BmxLiFa-3losfnMQg5QBJXyt_sZeHemqGRgKGZ1_YHd9n1soie5lVky-NxaoI2_58Ar4SofVtOqkobcEvlRZ1Q/s400/img2.png)
And the current in a loop 1/3 the radius of the earth required to create a field of that strength is
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8JWzdHzZJvEp3CsqEOP9n1ypA9YiBqkeIr-rBKeGEUr6JSpNtGMsDYghWSVTtMQujYOS0OxJUqcXMvPFcSKUsb2Mer5lHAutnql0KXaFmB3m5kzzkwrAn5k6XOtL6pjgfL4l8im6JPgw/s400/img3.png)
That's a lot of statcoulombs!
This is Problem 2.2 from Classical Electromagnetic Radiation
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