Considering the earth as a short magnet with its centre coinciding with the centre of earth, show that the angle of dip `phi` is related to magnetic latitude `lambda` through the relation `tan phi=2 tan lambda`

Explanation

To show that the angle of dip \( \phi \) is related to the magnetic latitude \( \lambda \) through the relation \( \tan \phi = 2 \tan \lambda \), we can follow these steps:

### Step 1: Understanding the Earth as a Magnet
Consider the Earth as a short magnet with its center coinciding with the center of the Earth. The magnetic field lines emerge from the North Pole and enter at the South Pole. The angle of dip \( \phi \) is the angle made by the resultant magnetic field with the horizontal plane.

### Step 2: Define Magnetic Latitude
The magnetic latitude \( \lambda \) is defined as the angle between the magnetic equator (where the magnetic field is horizontal) and the location of interest on the Earth's surface.

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