Question

What is the dipole magnetic field strength at the equator at geosynchronous orbit? (The equatorial field at the surface is 30,000 nT).

Answer 1

Solution-

The distance of geosynchronous  orbit from earth equator surface is 35,786 km.

Field strength at surface is 30,000 nT.

Consider North and South Pole of the earth act as poles of the magnet and use the magnetic field formula at the equatorial plane.

Here M is strength of one pole, l is half of distance between poles, r is distance between the center of dipole (center of earth ) and point of interest (where we want to know the magnetic field).

So from given value,

at the surface of earth, r=6400 km and l=6400

Now use the M value to find the magnetic field at distance r= 35786 + 6400 km= 42,186 km ( from center of earth),

therefore magnetic field intensity at 42186 km from earth center or 35786 km from earth surface due to its poles magnetic field is 2863.4 nT.