Question

At a certain place, the angle of dip is 30° and the horizontal component of earth’s magnetic field is 0.50 oerested. Theearth’s total magnetic field (in oerested) is(a) √3(b) 1(c) $\frac{1}{\sqrt{3}}$(d) $\frac{1}{2}$

Answer 1

Given At a certain place, the angle of dip is 30° and the horizontal component of earth’s magnetic field is 0.50 Oersted. The earth’s total magnetic field (in Oersted) is(a) √3(b) 1(c) \frac{1}{\sqrt{3}}(d) \frac{1}{2}

So we know that resultant intensity

         R = h / cos φ

We need to calculate the earth's total magnetic field

         R = 0.5 / cos 30

         R = 0.5 / √3 / 2

         R = 1 / 2 / √3 / 2

         R = 1 / √3  Oersted

So option c is correct

     

Answer 2

As, the angle made by the earth's total magnetic field with the horizontal direction is called angle of dip at the given place .

We can split the the intensity of the earth’s magnetic field  into two components -

Horizontal Component(H)  and Vertical Component(V)

Here, the angle of dip , ∅ = 30°

       The horizontal component of earth’s magnetic field ,H = 0.50 oersted.

Thus, according to the relation -

cos∅ = H/B

where, H = The horizontal component of earth’s magnetic field

            B = The earth’s total magnetic field

  =>  cos30 = 0.50/B

   =>  √3/2 = 0.50/B

    =>  B  =  1/√3 oersted

Thus, The earth’s total magnetic field , B = 1/√3  oersted

Thus, option (c) is correct .