In New Hampshire the average horizontal component of the...

In New Hampshire the average horizontal component of the Earth's magnetic field in 1912 was $16 \mu \mathrm{T}$ and the average inclination or "dip" was $73^{\circ} .$ What was the corresponding magnitude of the Earth's magnetic field?

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Key Concepts

Vector Decomposition

This concept involves breaking down a vector (in this case, the Earth's magnetic field) into its horizontal and vertical components using trigonometric functions. Understanding vector decomposition allows one to compute the magnitude of the original field when one component and the angle are known.

Magnetic Field Magnitude

This refers to the overall strength of the Earth's magnetic field. It is computed by combining its horizontal and vertical components, often through trigonometric relationships, to obtain the true field value.

Inclination (Dip) Angle

The inclination or dip angle is the angle at which the Earth's magnetic field tilts relative to the horizontal. It is crucial in determining how the field is oriented and in calculating the relationship between the horizontal component and the total field.

Trigonometric Relationships in Vector Analysis

Trigonometric functions, especially the cosine function in this context, are used to relate the horizontal component of the magnetic field to its overall magnitude. Knowing the cosine of the dip angle allows one to reverse-engineer the total magnitude from the horizontal measurement.

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