At a magnetic observation station, the horizontal component of the Earth's magnetic field … — JAMB UTME

At a magnetic observation station, the horizontal component of the Earth's magnetic field is $40\text{ }\mu\text{T}$ and the vertical component is $30\text{ }\mu\text{T}$ . What is the total magnetic field intensity of the Earth at this station in $\mu\text{T}$ ?

Answer: 50 μT

Answer

The total magnetic field intensity of the Earth at this station is

50\text{ }\mu\text{T}

The horizontal component (

B_h

) and vertical component (

B_v

) of the Earth's magnetic field act at right angles to each other. Therefore, the resultant total magnetic field intensity (

B

) is calculated using vector addition:

B = \sqrt{B_h^2 + B_v^2} = \sqrt{40^2 + 30^2} = 50\text{ }\mu\text{T}

Step-by-Step Solution

Identify the vector relationship between the horizontal and vertical components of the Earth's magnetic field.

B = \sqrt{B_h^2 + B_v^2}

, where

B_h = 40\text{ }\mu\text{T}

and

B_v = 30\text{ }\mu\text{T}

The horizontal and vertical components of the Earth's magnetic field are mutually perpendicular vector components.

Substitute the values into the formula and solve for total magnetic field intensity

B

B = \sqrt{(40)^2 + (30)^2} = \sqrt{1600 + 900} = \sqrt{2500} = 50\text{ }\mu\text{T}

Applying the Pythagorean theorem yields the magnitude of the resultant magnetic field vector.

Key Concept

Resolution of Earth's magnetic field into horizontal (

B_h

) and vertical (

B_v

) components.

Estimated Time:1m 0s

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