Question

The vertical and horizontal component of earth’s magnetic field at a place are $2\times {{10}^{-5}}T$and $3.464\times {{10}^{-5}}T$ respectively. Calculate the angle of dip and resultant earth’s magnetic field at that place.
(A) $\delta =60{}^\circ B=4\times {{10}^{-3}}T.$
(B) $\delta =30{}^\circ B=4\times {{10}^{-5}}T.$
(C) $\delta =15{}^\circ B=4\times {{10}^{-3}}T.$
(D) $\delta =30{}^\circ B=2\times {{10}^{-5}}T.$

Answer 1

Hint: We know that A magnetic field extends infinitely, though it weakens with distance from its source. The Earth's magnetic field, also called the geomagnetic field, which effectively extends several tens of thousands of kilometres into space, forms the Earth's magnetosphere. The intensity of the magnetic field is greatest near the magnetic poles where it is vertical. The intensity of the field is weakest near the equator where it is horizontal. The magnetic field's intensity is measured in gauss. The magnetic field has decreased in strength through recent years.

Complete step-by step answer:
We know that,
$\tan \theta =\dfrac{\text{horizontal field}}{\text{earth magnetic field}}$
Now we have to put the values in the above expression from the question, to get:
$\tan \theta =\dfrac{2\times {{10}^{-5}}}{3.464\times {{10}^{-5}}}=\dfrac{1}{1.732}=\dfrac{1}{\sqrt{3}}$
We know that
$\tan \theta =\dfrac{1}{\sqrt{3}}\Rightarrow \theta ={{30}^{{}^\circ }}$
The resultant field is given as:
Resultant field = $\dfrac{\text{horizontal field}}{\sin {{30}^{{}^\circ }}}$
So, after we put the values, we get that:
$\dfrac{2\times {{10}^{-5}}}{1/2}=4\times {{10}^{-5}}$
Hence, we can say that $\delta =30{}^\circ B=4\times {{10}^{-5}}T.$

So, the correct answer is option B.

Note: We know that the Earth's magnetic field is generated in the fluid outer core by a self-exciting dynamo process. Electrical currents flowing in the slowly moving molten iron generate the magnetic field. Angle of dip is also known as the magnetic dip and is defined as the angle that is made by the earth's magnetic field lines with the horizontal. When the horizontal component and the vertical component of the earth's magnetic field are equal, the angle of dip is equal to ${{45}^{{}^\circ }}$.
It should be known to us that the resultant forces are shown by the red arrows. The electric field line is the black line which is tangential to the resultant forces and is a straight line between the charges pointing from the positive to the negative charge. Since the electrostatic field is always directed away from positive charges and toward negative charges, field lines must go away from positive charges and toward negative ones.