The source of earth's magnetic field is best explained by

As we know that the Earth core is at high temperature and due to this high temperature the core of Earth contains large amount of molten metal.

Due to this large amount of molten metal there exist huge amount of charges or ions along with the molten metal. Now these molten metal or ions revolve around the axis of rotation of earth with the rotation of Earth around its own axis.

Due to this revolution of molten metal there exist a huge current in the earth due to motion of ions.

Now we know that magnetic field due to rotating current carrying coil is given by

so here this will produce magnetic field due to rotation of earth about its own axis.

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y