Question

At a place, the angle of dip is ${30^0}$ If the horizontal component of earth’s magnetic field is ${B_H}$ then the net field intensity at the place will be:
A. $\dfrac{{{B_H}}}{2}$
B. $\dfrac{{2{B_H}}}{{\sqrt 3 }}$
C. ${B_H}\sqrt 2 $
D. ${B_H}\sqrt 3 $

Answer 1

Hint: In order to solve this question, we should know that angle of dip is defined as the angle made by earth’s magnetic field line with the horizontal, here we will use the horizontal component of total intensity of magnetic field and by using the given value of different parameters, we will calculate the value of net field intensity at given point.

Complete step by step answer:
According to the question, we have given that the angle of dip as $\theta = {30^0}$ and let I be the net intensity of magnetic field of earth and as its given to us that horizontal component of magnetic field at that place is ${B_H}$ so, using the trigonometric cosine rule we know that horizontal component of net magnetic field intensity I can be written as
${B_H} = I\cos \theta $
on putting the values of $\theta = {30^0}$ we get,
${B_H} = I\cos {30^0}$
and we know that, $\cos {30^0} = \dfrac{{\sqrt 3 }}{2}$
so we get,
${B_H} = I\dfrac{{\sqrt 3 }}{2}$
$\Rightarrow I = \dfrac{{2{B_H}}}{{\sqrt 3 }}$
So, the value of intensity of earth’s magnetic field is $I = \dfrac{{2{B_H}}}{{\sqrt 3 }}$.

Hence, the correct option is B.

Note: It should be remembered that, intensity of magnetic field is the measurement of the force which the poles of a magnet experience when its placed in a magnetic field and It is measured in the units of amperes per metre which is written as $A{m^{ - 1}}$ and have a dimensional formula of $[{M^0}{L^{ - 1}}{T^0}A]$.