Moving Point Charge: Difference between revisions
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'''Solution:''' | '''Solution:''' | ||
1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >. | 1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >. | ||
2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do. | 2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation [[File:BiotSavartv.gif|150x200px]] tells us to do. | ||
Crossing these two, we get < 0, 0, 49200> | Crossing these two, we get < 0, 0, 49200> | ||
3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. | 3. The magnetic field will be this cross product multiplied by the charge of the proton <math> 1.6*10^{-19} </math> and divided by the magnitude of r squared. | ||
Revision as of 16:45, 1 December 2015
Page claimed by James Moroz Jmoroz3 (talk) 11:47, 20 November 2015 (EST)
This page covers the method of calculating the magnetic field from a moving point charge, derived from the Biot-Savart Law for magnetic fields.
The Main Idea
A Mathematical Model
The magnetic field of a moving point charge can be found using a derivation of the Biot-Savart Law for magnetic fields.
With this equation for the magnetic field given some current carrying object, we can rewrited Idl in terms of velocity in order to relate the velocity of the moving particle to the magnetic field at an observation location a distance r from this particle.
With this substitution, the final formula comes out to be:
where q is the charge of the particle, v is the velocity of the moving particle, and r is the distance from the observation location to the moving particle.
Examples
Be sure to show all steps in your solution and include diagrams whenever possible
Simple
At a particular instant, a proton at the origin has velocity < 4e4, -3e4, 0> m/s. Calculate the magnetic field at location < 0.03, 0.06, 0 > m, due to the moving proton.
Solution:
1. The first we need to do is find r hat. Given the vector <0.03, 0.06, 0>, we can calculate the normalized r hat vector to be < 0.447, 0.894, 0 >.
2. Once we have both the velocity and r hat vectors, we can take the cross product of these two as the equation tells us to do.
Crossing these two, we get < 0, 0, 49200>
3. The magnetic field will be this cross product multiplied by the charge of the proton [math]\displaystyle{ 1.6*10^{-19} }[/math] and divided by the magnitude of r squared.
The final answer will be [math]\displaystyle{ \lt 0, 0, 1.75*10^{-19}\gt }[/math]
Middling
The electron in the figure below is traveling with a speed of
[math]\displaystyle{ v = 5*10^6 }[/math]m/s. What is the magnitude of the magnetic field at location A if r = [math]\displaystyle{ 8*10^{-10} }[/math]m and [math]\displaystyle{ \theta=40 }[/math]degrees
Difficult
An electron is moving horizontally to the right with speed [math]\displaystyle{ 5*10^6 }[/math] m/s. What is the magnetic field due to this moving electron at the indicated locations in the figure? Each location is d = 7 cm from the electron, and the angle θ = 35°. Give both magnitude and direction of the magnetic field at each location.
Connectedness
A single moving point charge represents the most simple situation of charges moving in space to produce a magnetic field. In reality, this situation rarely occurs, however understanding how a single moving point charge interacts to produce a field will allow you to understand how sets of moving charges produce a field in space as well.
History
The history of the Biot Savart law and its discovery can be found at the Biot-Savart Law.
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
http://maxwell.ucdavis.edu/~electro/magnetic_field/pointcharge.html This section contains the the references you used while writing this page