Question

At a certain place, the angle of dip is 60° and the horizontal component of the Earth’s magnetic field is 0.2 × 10^-4 T. Calculate the vertical component (in T) of the Earth’s magnetic field? (tan 60° = $\sqrt{3}$ )

• A. $2\sqrt{3}\times {10}^{-4}$
• B. $2\sqrt{3}$
• C. $2\sqrt{3}\times {10}^{-5}$
• D. $\frac{\sqrt{3}}{2}\times {10}^{-3}$

Answer 1

The correct option is C

$2\sqrt{3}\times {10}^{-5}$

Step 1, Given data

The angle of dip = 60°

The horizontal component of the Earth’s magnetic field = 0.2 × 10^-4 T

Step 2, Finding the vertical component of the earth's magnetic field

We know,

$tan\alpha =\frac{Verticalcomponent}{Horizontalcomponent}$ where $\alpha$= angle of dip

Now putting all the values

$tan{60}^0=\frac{Veriticalcomponent}{0.2\times {10}^{-4}}$

After solving

$Verticalcomponent=2\sqrt{3}\times {10}^{-5}T$

Hence the correct option is (C): $2\sqrt{3}\times {10}^{-5}$T