On 25 December 2011, there were a number of attacks on Christmas Day during church services in northern Nigeria. There were bombings and shootings at churches in Madalla (near the capital, Abuja), Jos, Gadaka and Damaturu. At least 39 people were killed. The attacks were claimed by the Islamist group Boko Haram.
Albert Leo Schlageter
Albert Leo Schlageter (12 August 1894 — 26 May 1923) was a member of the German Freikorps. His activities sabotaging French occupying troops after World War I led to his arrest and eventual execution by French forces. His death created an image of martyrdom around him, which was cultivated by German nationalist groups, in particular the Nazi Party. During the Third Reich, he was widely commemorated as a national hero.
Magnetic reluctance
Magnetic reluctance, or magnetic resistance, is a measurement used in the analysis of magnetic circuits. It is like resistance in an electrical circuit, but rather than dissipating magnetic energy it stores magnetic energy. As an electric field causes an electric current to follow the path of least resistance, a magnetic field causes magnetic flux to follow the path of least magnetic reluctance. It is a scalar,
extensive quantity, like electrical resistance.
Reluctance is usually represented by ℜ.
The term was coined in May 1888 by Oliver Heaviside. The notion of “magnetic resistance” was first mentioned by James Joule and the term "magnetomotive force” (MMF) was first named by Bosanquet. The idea for a magnetic flux law, similar to Ohm's law for closed electric circuits, is attributed to H. Rowland.
The total reluctance is equal to the ratio of the "magnetomotive force” (MMF) in a passive magnetic circuit to the magnetic flux in this circuit. In an AC field, the reluctance is the ratio of the amplitude values for a sinusoidal MMF and magnetic flux. (see phasors)
The definition can be expressed as:
where
It is sometimes known as Hopkinson's law and is analogous to Ohm's Law with resistance replaced by reluctance, voltage by MMF and current by magnetic flux.
Magnetic flux always forms a closed loop, as described by Maxwell's equations, but the path of the loop depends on the reluctance of the surrounding materials. It is concentrated around the path of least reluctance. Air and vacuum have high reluctance. Easily magnetized materials such as soft iron have low reluctance. The concentration of flux in low-reluctance materials forms strong temporary poles and causes mechanical forces that tend to move the materials towards regions of higher flux so it is always an attractive force (pull).
The reluctance of a uniform magnetic circuit can be calculated as:
or
where
The inverse of reluctance is called "permeance".
Its SI derived unit is the henry (the same as the unit of inductance, although the two concepts are distinct).
Reluctance can also be applied to:
Triglav
Triglav is a mountain in the Alps. It is the highest mountain in Slovenia. It is also the highest peak of the Julian Alps, in the southeastern part of the Alps.
Its name means "three-headed" in Slovene. While this can describe the mountain, it is more likely the mountain was named for the Old Slovene god, Triglav. The mountain is shown on the Flag of Slovenia.
This mountain is in a national park.
Ampère's circuital law
Ampère's circuital law, discovered by André-Marie Ampère in 1826, relates the magnetic field around a closed loop to the electric current passing through the loop. It is now one of Maxwell's equations, which form the basis of classical electromagnetism.
The law relates magnetic fields to electric currents that produce them. A scientist can use Ampere's law to determine the magnetic field associated with a given current or current associated with a given magnetic field, if there is no time changing electric field present.
In its original form, Ampère's Circuital Law relates the magnetic field to its electric current source.
The law can be written in two forms, the "integral form" and the "differential form". The forms are equivalent, and related by the Kelvin–Stokes theorem. It can also be written in terms of either the B or H magnetic fields. Again, the two forms are equivalent (see the "proof" section below).
Ampère's circuital law is now known to be a correct law of physics in a magnetostatic situation: The system is static except possibly for continuous steady currents within closed loops. In all other cases the law is incorrect unless Maxwell's correction is included (see below).
In SI units (the version in cgs units is in a later section), the "integral form" of the original Ampère's circuital law is:
or equivalently,
where
See below for further explanation of the curve "C" and surface "S". There are a number of ambiguities in the above definitions that require clarification and a choice of convention.
First, three of these terms are associated with sign ambiguities: the line integral formula_5 could go around the loop in either direction (clockwise or counterclockwise); the vector area dS could point in either of the two directions normal to the surface; and "I" is the net current passing through the surface "S", meaning the current passing through in one direction, minus the current in the other direction—but either direction could be chosen as positive. These ambiguities are resolved by the right-hand rule: With the palm of the right-hand toward the area of integration, and the index-finger pointing along the direction of line-integration, the outstretched thumb points in the direction that must be chosen for the vector area dS. Also the current passing in the same direction as dS must be counted as positive. The right hand grip rule can also be used to determine the signs.
Second, there are infinitely many possible surfaces "S" that have the curve "C" as their border. (Imagine a soap film on a wire loop, which can be deformed by moving the wire). Which of those surfaces is to be chosen? If the loop does not lie in a single plane, for example, there is no one obvious choice. The answer is that it does not matter; it can be proven that any surface with boundary "C" can be chosen.
By the Kelvin–Stokes theorem, this equation can also be written in a "differential form". Again, this equation only applies in the case where the electric field is constant in time; see below for the more general form. In SI units, the equation states:
where
The electric current that arises in the simplest textbook situations would be classified as "free current." For example, the law can apply to the current that passes through a wire or battery. In contrast, "bound current" arises in the context of bulk materials that can be magnetized and/or polarized. (All materials can to some extent.)
When a material is magnetized (for example, by placing it in an external magnetic field), the electrons remain bound to their respective atoms, but behave as if they were orbiting the nucleus in a particular direction, creating a microscopic current. When the currents from all these atoms are put together, they create the same effect as a macroscopic current, circulating perpetually around the magnetized object. This magnetization current J is one contribution to "bound current".
The other source of bound current is bound charge. When an electric field is applied, the positive and negative bound charges can separate over atomic distances in polarizable materials, and when the bound charges move, the polarization changes, creating another contribution to the "bound current", the polarization current J.
The total current density J due to free and bound charges is then:
with J the "free" or "conduction" current density.