At a place horizontal and vertical components of earth's magnetic fiel...
Calculation of Dip Angle and Declination
Horizontal and Vertical Components of Earth's Magnetic Field
Given:
- BH = 1G, 10 west of north
- BV = 1G, vertically downward
Calculation of Total Magnetic Field
The total magnetic field can be calculated using the Pythagorean theorem as:
BT = √(BH2 + BV2)
Substituting the given values, we get:
BT = √((1G)2 + (1G)2) = √2G
Calculation of Dip Angle
The dip angle (δ) can be calculated using the following formula:
tan δ = BV/BH
Substituting the given values, we get:
tan δ = 1G/1G = 1
Using a calculator, we can find that δ = 45°
Calculation of Declination
The declination (δ°) can be calculated using the following formula:
tan δ° = BH/(BT * cos δ)
Substituting the given values, we get:
tan δ° = (1G)/(√2G * cos 45°) = 1
Using a calculator, we can find that δ° = 45° west
Explanation
Earth's magnetic field has both horizontal and vertical components. The horizontal component (BH) is the component that is parallel to the surface of the earth, while the vertical component (BV) is the component that is perpendicular to the surface of the earth.
The total magnetic field (BT) can be calculated using the Pythagorean theorem, as it is the magnitude of the vector sum of the horizontal and vertical components.
The dip angle (δ) is the angle between the direction of the total magnetic field vector and the horizontal plane. It can be calculated using the tangent of the angle between the vertical and horizontal components.
The declination (δ°) is the angle between the direction of the total magnetic field vector and true north. It can be calculated using the tangent of the angle between the horizontal component and the projection of the total magnetic field vector onto the horizontal plane.