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

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Applications

Magnetic Response

The Biot-Savart law has applications in nuclear magnetic resonance (NMR) spectroscopy, used to measure the chemical signals given off by compounds. The law can be used to calculate the magnetic responses at the atomic or molecular level, provided that the current density can be obtained mathematically. For more about NMR spectroscopy, see the wiki page [1]

Aerodynamics

In aerodynamics, the Biot-Savart law may be used to calculate the velocity induced by vortex lines, which are lines that are everywhere tangent to the vorticity vector. A vorticity vector is a pseudovector field that describes the tendency of something to rotate, in other words, the curl of the velocity field of a fluid.

In this example,[2], the yellow arms represent whirring space from a black hole and the red lines represent vortex lines. Astrophysicists may use the Biot-Savart Law to calculate the velocity.

History

Felix Savart was born on June 30, 1791 in Mezieres, France to a family with a strong association with military engineering schools. While completing his formal education in 1808 at the university in Metz, Savart decided to pursue medicine and become a physician. After serving a short stint in Napoleon's army in the the first engineering battalion, he resumed his medical training and graduated from Strasbourg in 1816. During his medical studies, Savart became interested in first century Roman writer Aulus Cornelius Celsus and his famous medical book De medicinia. Savart began working on a translation and set up a medical practice, but gradually became more interested in physics than patients.

See also

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

Further reading

Books, Articles or other print media on this topic

External links

Internet resources on this topic

References

This section contains the the references you used while writing this page