Magnetic dip, dip angle, or magnetic inclination is the angle made with the horizontal by the
Earth's magnetic field lines. This angle varies at different points on the Earth's surface. Positive values of inclination indicate that the magnetic field of the Earth is pointing downward, into the Earth, at the point of measurement, and negative values indicate that it is pointing upward. The dip angle is in principle the angle made by the needle of a vertically held compass, though in practice ordinary compass needles may be weighted against dip or may be unable to move freely in the correct plane. The value can be measured more reliably with a special instrument typically known as a
dip circle {{Refimprove, date=November 2011
Dip circles (also ''dip needles'') are used to measure the angle between the horizon and the Earth's magnetic field (the dip angle). They were used in surveying, mining and prospecting as well as for the demonst ...
.
Dip angle was discovered by the engineer
Georg Hartmann
Georg Hartmann (sometimes spelled Hartman; February 9, 1489 – April 9, 1564) was a German engineer, instrument maker, author, printer, humanist, priest, and astronomer.
Early life and studies
Hartmann was born in Eggolsheim near Forchheim, p ...
in 1544. A method of measuring it with a dip circle was described by
Robert Norman
Robert Norman was a 16th-century-English mariner, compass builder, and hydrographer who discovered magnetic inclination, the deviation of the Earth's magnetic field from the vertical.
Work
Robert Norman is noted for ''The Newe Attractive'' ...
in England in 1581.
Explanation
Magnetic dip results from the tendency of a magnet to align itself with lines of magnetic field. As the Earth's magnetic field lines are not parallel to the surface, the north end of a compass needle will point upward in the southern hemisphere (negative dip) or downward in the northern hemisphere (positive dip) . The range of dip is from -90 degrees (at the
South Magnetic Pole) to +90 degrees (at the
North Magnetic Pole
The north magnetic pole, also known as the magnetic north pole, is a point on the surface of Earth's Northern Hemisphere at which the Earth's magnetic field, planet's magnetic field points vertically downward (in other words, if a magnetic comp ...
). Contour lines along which the dip measured at the Earth's surface is equal are referred to as
isoclinic line
A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a plane section of the three-dimensional grap ...
s. The locus of the points having zero dip is called the ''magnetic equator'' or
aclinic line
A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a plane section of the three-dimensional gra ...
.
Calculation for a given latitude
The inclination
is defined locally for the magnetic field due to the Earth's core, and has a positive value if the field points below the horizontal (ie into the Earth). Here we show how to determine the value of
at a given latitude, following the treatment given by Fowler.
Outside Earth's core we consider Maxwell's equations in a vacuum,
and
where
and the subscript
denotes the core as the origin of these fields. The first means we can introduce the scalar potential
such that
, while the second means the potential satisfies the
Laplace equation
In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as
\nabla^2\! f = 0 or \Delta f = 0,
where \Delta = \nab ...
.
Solving to leading order gives the magnetic dipole potential
and hence the field