A magnetic needle free to rotate about the vertical direction (compass ) point 3.5 west of the geographic north . Another magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at `18^(@) `with the horizontal . The magnitude of the horizontal component of the earth ' magnetic field at the place is known to be 0.40 G . what is the direction and magnitude of the earth's magnetic field at the place ?