Magnetic Field of a Long Thick Wire Using Ampere's Law: Difference between revisions
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To find the magnetic field at a distance r from the center of the long wire apply Ampere's Law. | To find the magnetic field <math>B</math> at a distance <math>r</math> from the center of the long wire apply Ampere's Law. By the symmetry of the wire <math>B</math> will always be constant and tangential to the circular path at every point around the wire. | ||
d<math>{\vec{l}}</math> | |||
The path integral <math>{{\oint}d\vec{l}}</math> in this situation is equal to the circumference of the circular path around the wire. This is equal to <math>2πr</math>. | |||
Using the formula above and plugging in <math>{d\vec{l}}</math> we have: <math>{B(2πr) = μ_0I}</math>. To solve for <math>B</math> divide both sides by <math>2πr</math>. | |||
This results in the equation: <math>{B = \frac{μ_0I}{2πr}}</math> which is equal to <math>{\frac{μ_02I}{4πr}}</math>. This is the equation for the magnetic field of a long thick wire that is found using the Biot-Savart law. | |||
==Connectedness== | ==Connectedness== | ||
Revision as of 22:24, 1 December 2015
claimed by Baron Hall
The Main Idea
This section explains how to find the magnetic field near a long thick wire using Ampere's Law. Finding the magnetic field using Ampere's Law is very simple compared to finding it using the Biot-Savart law.
Formula for Ampere's Law
How to Find Magnetic Field of A Long Thick Wire
To find the magnetic field [math]\displaystyle{ B }[/math] at a distance [math]\displaystyle{ r }[/math] from the center of the long wire apply Ampere's Law. By the symmetry of the wire [math]\displaystyle{ B }[/math] will always be constant and tangential to the circular path at every point around the wire.
The path integral [math]\displaystyle{ {{\oint}d\vec{l}} }[/math] in this situation is equal to the circumference of the circular path around the wire. This is equal to [math]\displaystyle{ 2πr }[/math].
Using the formula above and plugging in [math]\displaystyle{ {d\vec{l}} }[/math] we have: [math]\displaystyle{ {B(2πr) = μ_0I} }[/math]. To solve for [math]\displaystyle{ B }[/math] divide both sides by [math]\displaystyle{ 2πr }[/math].
This results in the equation: [math]\displaystyle{ {B = \frac{μ_0I}{2πr}} }[/math] which is equal to [math]\displaystyle{ {\frac{μ_02I}{4πr}} }[/math]. This is the equation for the magnetic field of a long thick wire that is found using the Biot-Savart law.
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