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# Biot-Savart Law

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## Jeffrey Huang

on 22 May 2015

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#### Transcript of Biot-Savart Law

History and essential knowledge
Variables
• dB - magnetic flux density (how much magnetic field is going through an area)
• I - current
• dl - length of a segment of wire (point current element)
• sin(θ) - direction of the current
• r - distance between point and current element
• k - Coulomb's constant
• µ - magnetic permeability (ability of a material to support the formation of a magnetic field)
• θ - the angle formed between l and r
Relationship to Coulomb's Law
Coulomb's Law for an Electric Field
What is the magnetic field at point P?
What is the magnetic field at point A?
Ampère's Law
Biot-Savart Law
1. Jean-Baptiste Biot
•1774-1862
• optics, magnetism, astronomy
• collaborated with Louis Pasteur

2. Félix Savart
• Savart's wheel,
savart
= musical interval

3. Currents running through wires create magnetic fields

4. Consistent with Ampère's circuital law and Gauss's law for magnetism
“My boy, I have loved science so much during my life, that this touches my very heart!”
-Jean Baptiste Biot
Plug in values...
(semi-circlular section of wire)
Biot-Savart Law:
(circular section of wire)
Circular Wire Model
Plug in values...
Solenoids
Electromagnets
A long coil of wire consisting of many loops is called a
solenoid
.
The formula for the magnetic field for a solenoid can be derived from Ampère's Law.
If a piece of iron is placed within a solenoid, it will greatly multiply the magnetic field, creating an
electromagnet
.
A type of magnet that has a magnetic field produced by an electric current is called an
electromagnet.
Used in motors, bells, generators, headphones, MRI machines, etc.
Created by solenoids
Full transcript