Biot-Savart Law

The Biot-Savart Law is an equation that describes the quantitative relationship between an electrical current and the magnetic field it generates. This law is seen as a magnetic equivalent of Coulomb's Law, and states that the magnetic field decreases with the square of a distance from a point of current.Page in progress by Andrea Boyd. [contd]

The Main Idea

An electron current flowing through a conductor, such as a wire, or a moving electric charge produces a detectable magnetic field. The Biot-Savart law describes this phenomenon by relating the magnetic field to the magnitude, direction, length, and proximity of the electric current.

A Mathematical Model

The general formula for a single charge is [math]\displaystyle{ \vec B=\frac{\mu_0}{4\pi}\frac{q\vec v\times\hat r}{r^2} }[/math] where [math]\displaystyle{ \mu_0 }[/math] is the constant [math]\displaystyle{ 1e-7 \frac{tesla * m^2}{coloumb * \frac{m}{s}} }[/math] exactly. [math]\displaystyle{ \vec q }[/math] is the velocity of the point charge [math]\displaystyle{ q }[/math] and [math]\displaystyle{ \hat r }[/math] is the unit vector pointing from the source towards the observation location (remember [math]\displaystyle{ r= r(obs)-r(source) }[/math])

Additionally, in problems where the angle is given, another form of the Biot-Savart law may be used: [math]\displaystyle{ B=\frac{\mu_0}{4\pi}\frac{qv sin(\theta)}{r^2} }[/math]

A Computational Model

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Examples

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History

In 1820 two Frenchman, Felix Savart and Jean-Baptiste Biot, published Note sur le magnétisme de la pile de Volta and presented it to the Academy of Sciences in what became known as the Biot-Savart Law. Savart had been trained as a medical doctor, but began focusing more on physics rather than patients. He became interested in acoustics, building his own violins and conducting research on sound, and attended a lecture in Paris given by French mathematician, Jean-Baptiste Biot.

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