A compass needle oscillates 20 times per minute at a place where the dip is `45^@` and 30 times per minute where the dip is `30^@`. Compare the total magnetic field due to the earth at the two places.

Explanation

To solve the problem of comparing the total magnetic field due to the Earth at two different places with varying dip angles, we can follow these steps:

### Step 1: Understand the relationship between oscillations and magnetic field
The oscillation frequency of a compass needle is related to the magnetic field strength. The number of oscillations per minute (N) is inversely proportional to the square root of the magnetic field (B). Therefore, we can express this relationship as:
\[ N \propto \frac{1}{\sqrt{B}} \]
This implies that:
\[ B \propto \frac{1}{N^2} \]

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