At a certain place the angle of dip is 30° and the horizontal component of earth's magnetic field is 0.5 G. The earth's total magnetic field (in G), at that certain place, is :

Solution

Physics sir · 3 steps

The horizontal component is the cosine part of the total field, so divide 0.5 G by cos 30°.

1. What dip means. The angle of dip δ is the angle the total field B makes with the horizontal. Measured from the horizontal, the horizontal component is the adjacent side, so it takes the cosine.

   B_H = B cos δ ⇒ B = B_H/(cos δ)

2. Put in numbers. cos 30° = √3/2, so B = 0.5/(√3/2) = 1/√3 G ≈ 0.58 G.
3. So. The total field is 1/√3 G, option (a). It is larger than B_H, as a total field must be.

The idea to keep. Dip is measured from the horizontal: B_H = B cos δ and B_V = B sin δ. The total field is always at least as large as either component.

Answer from the NTA final answer key. Solution by PrepWiser.