Question

The angle of dip at the place where the horizontal and vertical component of earth magnetic field are equal to
A. $45^\circ $
B. $30^\circ $
C. $0^\circ $
D. $60^\circ $
E. $90^\circ $

Answer 1

Hint: In science, the magnetic field can be described as the specific area around a magnetic material. In the magnetic field, when the conductor moves up and down, it means the conductor cuts the magnetic flux. By dividing the equation of vertical component of earth magnetic field with horizontal component of earth magnetic field we can arrive at the formula for angle of dip. By using that formula we can arrive at the answer for the angle of dip at the place where the horizontal and vertical component of earth's magnetic field when both the cases are equal.


Useful formula:
The equation for finding the horizontal component of earth’s magnetic field is given as,
${B_h} = B\cos \theta $
Where ${B_h}$is the horizontal component of the earth magnetic field, $B$net magnetic field $\theta $is the angle of dip.
The equation for finding the vertical component of earth’s magnetic field is given as,
${B_v} = B\sin \theta $
Where ${B_v}$is the vertical component of the earth magnetic field, $B$ net magnetic field $\theta $is the angle of dip.
Given data
The horizontal and vertical component of earth magnetic field are equal that is ${B_h} = {B_v}$

Complete step-by-step answer:
The expression for finding the vertical component of electric field is given as,
${B_v} = B\sin {\theta _v}......(1)$
The equation for finding the horizontal component of earth’s magnetic field is given as,
${B_h} = B\cos \theta ......(2)$

Divide equation (2) by (1)
$
  \dfrac{{{B_v} = B\sin \theta }}{{{B_h} = B\cos \theta }} \\
  \theta = {\tan ^{ - 1}}\left( {\dfrac{{{B_v}}}{{{B_h}}}} \right) \\
  {B_v} = {B_h} \\
  \theta = {\tan ^{ - 1}}\left( 1 \right) \\
  \theta = 45^\circ \\
 $

Hence, the option A is correct.

Additional information: The components that affect the magnitude and the direction of the earth’s magnetic field are Magnetic declinations, Angle of dip and the horizontal component of the earth’s magnetic field.
The horizontal component of the earth’s magnetic field is the projection of the magnetic field of the earth on its surface. The vertical component of the electric field at the equator is zero.

Note: The angle of dip arrived from the horizontal and vertical component of the earth magnetic field, and the vertical component is derived from the net magnetic field. The range of the angle of dip ranges from the north pole to south pole that is from to 90 degree to – 90 degree. The horizontal component of the earth magnetic field equals the net magnetic field in the case of when the angle of the dip is zero.