If a magnet is suspended at an angle of 30 ∘ to the earth magnetic meridian , the dip needle makes angle of 45 ∘ with the horizontal . the real dip is ?

Question

If a magnet is suspended at an angle of       30          ∘       to the earth magnetic meridian , the dip needle makes angle of       45          ∘       with the horizontal . the real dip is ?

pawia6g · Accepted Answer

Let the vertical component of earth&#039;s magnetic field be V and its horizontal component at magnetic meridian be H.Then the angle of dip   θ at magnetic meridian will be given by  tan  ⁡  θ  =      V    H  ...[1]When the dip needle is suspended at an angle of       30          ∘       to the earth magnetic meridian then it makes an angle       45          ∘       with the horizontal.In this situation vertical component of earth&#039;s field responsible for its orientation with the horizontal direction, remains same as V but the component in horizontal direction becomes   H  cos  ⁡      30          ∘      So   tan  ⁡      45          ∘        =      V          H      cos      ⁡              30                  ∘                      ⇒      V    H    =  cos  ⁡      30          ∘      ...[2]Comparing [1] and [2] we get  tan  ⁡  θ  =  cos  ⁡      30          ∘        =            3        2    ⇒  θ  =      tan          −      1        ⁡  (            3        2    )  ≈      40.9          ∘

If a magnet is suspended at an angle of 30 to the earth magnetic meridian , the dip needle makes angle of 45 with the horizontal . the real dip is ?

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