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 ?

Answer

`0.42 G` , directed at angle is `18^(@)` with horizontal in the magnetic meridian towards the ground