Physics Book - User contributions [en]

Conductors

2025-04-13T18:34:22Z

David2212: claim

Claimed by '''David Nam Spring 2025''', in progress

Conductor are materials that allow electric current to travel with little resistance throughout. This is related to the structure of the atoms of the conductor. In this section, we will look at what a conductor is, why it is this way, and the applications.

==The Main Idea==

Conductors are defined as a material that allows for charged particles to move easily throughout. Charges placed on the surface of a conductor will not simply stay in one spot or only spread over the surface, but will immediately spread evenly throughout the conductor- given there are no interfering forces. If the conductor is in an electric field, for example, it will cause the (negative) charges to move in the opposite direction of the field.

Electric current flows by the net movement of electric charge. This can be by electrons, ions, or other charged particles.

Conductors allow for easy movement of charged particles because of the structure of the atoms. The outermost electrons in atoms that make up conductors are only loosely bound and allow for more interaction with other particles. These electrons that are free to move about the conductor are called the "sea of electrons". The sea of electrons is therefore able to move in response to other charges that are put on the conductor or in response to an electric field that the conductor is within. A conductor in an electric field will have an almost instantaneous rearranging of electrons so that there is a net zero electric field within the conductor. The external electric field induces an equal and opposite electric field within the conductor, so the two fields cancel out for a net zero electric field.

[[File:Cross section and length image.gif|right|180 px]] There are some factors that can change the conductance of a conductor. Shape and size, for example, affect the conductance of an object. A thicker(larger cross sectional area A as shown in the diagram) piece will be a better conductor than a thinner piece of the same material and other dimensions. This is the same concept that a thicker piece of wire allows for greater current flow. The larger cross sectional area allows for more flow of charge carriers. A shorter conductor will also conduct better since it has less resistance than a longer piece. Conductance itself can also change conductivity. In actively conducting electric current, the conductor heats up. This is secretly the third factor affecting conductance: temperature. Changes in temperature can cause the same object to have a different conductance under otherwise identical conditions. The most well known example of this is glass. Glass is more of an insulator at typical to cold temperatures, but becomes a good conductor at higher temperatures. Generally, metals are better conductors at cooler temperatures. This is because an increase in temperature is an increase in energy, specifically for electrons.

[[File:Conductor chart.gif|600 px]]

===A Mathematical Model===

Ohm's Law of J = σE can be used to model the relationship of conductivity to electric current density where J is electric current density, σ is conductivity of the material, and E is electric field. This is a generalized form of the well known V = IR.

σ is larger for better conductors like metals and saltwater. For "perfect" conductors, σ approaches infinity. In this case, E would be zero since the current density J cannot be infinity.

Materials are generally divided into three categories based on σ:
*Lossless Materials: σ = 0
*Lossy Materials: σ > 0
*Conductors: σ >> 0

Below is a breakdown of how conductivity is calculated. This could be considered a formula for conductivity, but it would be more accurate to think of it as a definition.

[[File:Electric conductivity equation.jpg|400 px]]

Conductivity can also be explained as the inverse of resistivity. σ = 1/ρ where ρ is resistivity.

===A Computational Model===

[[File:Conductor computational model.PNG|right|400 px]]

[http://www.physics-chemistry-interactive-flash-animation.com/electricity_electromagnetism_interactive/electric_conductors_insulators.htm This simple interactive] is a great way to see which real objects are made of conducting or insulating material. Try to guess which objects will allow for flow of electricity before you test with the interactive.

https://phet.colorado.edu/en/simulation/semiconductor

==Examples==

===Simple===
Material A has a resitivity of <math> 5.90 \cdot 10^{-8} Ω \cdot m </math> and Material B has a conductivity of <math> 1.00 \cdot 10^7 S/m </math>. They are the same size and temperature. Which is a better conductor?

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution</div>
<div class="mw-collapsible-content">

We can change Material A's resitivity to conductivity with the formula σ = 1/ρ. σ = <math>\frac{1}{(5.90 \cdot 10^{-8} Ω \cdot m)} = 1.69 \cdot 10^7 S/m</math>. Since Material A has a greater conductivity, it is a better conductor.

These numbers are the real conductivities of Zinc(Material A) and Iron(Material B).

</div></div>

===Middling===
A negatively charged iron block is placed in a region where there is an electric field downward (in the -y direction). What will be the charge distribution of the iron block in this field? (Problem 47 from Matter and Interactions, page 583)

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution</div>
<div class="mw-collapsible-content">

[[File:Conductor question diagram.jpg|300 px]]

Remember that in the direction of an electric field is traditionally the direction of positive charge movement. Since the iron block is a conductor, it has electrons that are free to move and will travel opposite the direction of the electric field. This will leave an excess of positive charge at the bottom of the block and an excess of negative charge at the top of the block, as shown in the diagram.

</div></div>

===Difficult===
This should be completed by a student

<div class="toccolours mw-collapsible mw-collapsed" style="width:800px; overflow:auto;">
<div style="font-weight:bold;line-height:1.6;">Solution</div>
<div class="mw-collapsible-content">

solution

</div></div>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Modern research on electricity and conductors starts in the 1700s. Many different scientists contributed to the research that led to the understanding and use of conductors. Stephan Gray was one of the first of these, first studying the idea of electricity and then conductors. In Gray's time, the general consensus was that "electric virtue" was a quality that some materials could attain and others could not. Some materials, like glass, could acquire electric virtue by friction, while others, like metal, could be given electric virtue by contact with a charged object. Gray tested this theory with many different types of material, even with a child(who did work as a conductor).

Dufay began research on the same topics of charge transfer and conductance just after Gray. He lengthened the list of objects that could be given electric virtue by friction. Dufay also named the growing categories. "Electrical bodies" were what we call insulators and "non-electric bodies" were what we know as conductors. While this seems backwards from the way we think about insulators and conductors, it comes from the idea that electric virtue was intrinsic to insulators because charge could be induced on these simply by friction, while conductors can only come to have a charge by contact with a charged insulator.

Only when Benjamin Franklin came around some later did the ideology and vocabulary make a big switch. Franklin suggested that electricity is not created by electrical bodies through friction, but that it is a fluid shared by all bodies and can pass between them. Franklin also caused the shift in language from non-electric bodies to conductors and electric bodies to non-conductors.

There is some evidence that ancient Egyptians also used electricity.

== See also ==

===Further reading===

To learn more about conductors:
*[[Polarization of a conductor]]
*[[Charged Conductor and Charged Insulator]]
*[[Field of a Charged Ball]]

===External links===

*https://www.youtube.com/watch?v=BY8ZPobU8B0
*https://www.khanacademy.org/science/ap-physics-1/ap-electric-charge-electric-force-and-voltage/conservation-of-charge-ap/v/conductors-and-insulators
*https://www.youtube.com/watch?v=PafSqL1riS4

==References==

*https://en.wikipedia.org/wiki/Electrical_conductor

*https://www.thoughtco.com/examples-of-electrical-conductors-and-insulators-608315

*https://www.rpi.edu/dept/phys/ScIT/InformationProcessing/semicond/sc_glossary/scglossary.htm

*http://maxwells-equations.com/materials/conductivity.php

*https://en.wikipedia.org/wiki/Ohm%27s_law

*https://www.youtube.com/watch?v=BY8ZPobU8B0

*https://www.physicsclassroom.com/class/estatics/Lesson-1/Conductors-and-Insulators

*http://histoires-de-sciences.over-blog.fr/2018/04/history-of-electricity.the-discovery-of-conductors-and-insulators-by-gray-dufay-and-franklin.html

*Benjamin, Park. A History of Electricity (The Intellectual Rise of Electricity) from Antiquity to the Days of Benjamin Franklin. J. Wiley & Sons, 1898. Google Books, https://books.google.com/books?hl=en&lr=&id=K2dDAAAAIAAJ&oi=fnd&pg=PR1&dq=ancient egypt electricity&ots=edMffcocC0&sig=zFX9kUz2FKoPcPTCf8YVId2AjhQ#v=onepage&q&f=false.

*https://www.thoughtco.com/table-of-electrical-resistivity-conductivity-608499

[[Category:Which Category did you place this in?]]

Magnetic Field of a Long Straight Wire

2025-04-13T18:21:57Z

David2212: /* GlowScript Code Example: Wire Interaction */

Edited by Tyrone Xu (Spring 2025)

==History==
The magnetic field of a wire was first discovered during an experiment by '''Hans Christian Oersted''' (1777-1851) of Denmark in 1820. This experiment consisted of running a current through a wire and placing a compass underneath it to see if there was any effect. The effect he found changed the world forever: he had discovered the important relationship between electricity and magnetism. Before this, the world had taken note of the similarities between electricity and magnetism but nobody had truly "proved" this relationship up until this point. Oersted then went on to write his groundbreaking scientific paper "Experiments on the effect of a current of electricity on the magnetic needle," which shocked and awed the rest of the scientific world. This experiment laid the foundation for what we now study in electromagnetism courses, such as Physics II. While this finding falls directly into the category of "Magnetic Field of a Long Straight Wire," it also may very well be the most important discovery by any physicist in history (this is up for debate but this is just my opinion on the topic; nonetheless, it is extremely crucial).

==Summary==
A long straight wire, that is carrying some current I, will generate it's own magnetic field. The shape of the magnetic field will be concentric circles centered around the wire. The magnetic field lines are identical and the spacing of these lines increases as the distance increased. The direction of the magnetic field lines can be observed by placing small compass needles on a circle close to the wire. If there is no current, then the needles will align with the Earth's magnetic field and if there is a current, then the needles will point tangent to the circle. If the wire is vertical and the current is facing upwards, then on the left side of the wire, the magnetic field will come out towards you. On the right side of the wire, the magnetic field would go in towards the other direction. If the current was going downwards, then the magnetic field would reverse directions but would still be in concentric circles around the wire. The second form of the right hand rule in terms of the wire would be used so that the thumb is going in the direction of the current, and the fingers will go in the direction of the magnetic field. The closer you get to the wire, the stronger the magnetic field. The further you get from the wire, the weaker the magnetic field. As the magnetic field gets spread out, it is distributed over a wider circumference. The mathematical interpretation of the magnetic field is detailed below.

==Models==

===Mathematical Model===
Imagine centering a wire of length <math>L</math> on the y-axis, and having a current <math>I</math> run through the wire in the +y direction. We are interested in finding the magnetic field at some point along the z axis, say <math> (0,0,z) </math>.

From here, we use the Biot-Savart Law:

::<math> d\mathbf{B} = \frac{\mu_{0}}{4\pi} \frac{I d\mathbf{L} \times \mathbf{\hat r}}{r^2}</math>

In our case, <math>\mathbf{\hat r}</math> is simply a unit vector in the direction of a point along the wire <math>(0,y,0)</math> to a point along the z-axis <math>(0,0,z)</math>. This can be represented by:

::<math>\mathbf{\hat r} = \frac{\mathbf{r}}{|\mathbf{r}|} = \frac{(0,0,z) - (0,y,0)}{\left|(0,0,z) - (0,y,0) \right|} = \frac{(0,-y,z)}{\left|(0,-y,z)\right|} = \frac{(0,-y,z)}{\sqrt{y^2 + z^2}}</math>

In our case, <math>d\mathbf{L}</math> is simply a vector pointing along a length of the wire. Since our wire is solely along the y-axis, this can be reduced as follows:

::<math>d\mathbf{L} = d \Bigr[(0,y,0)\Bigr] = (0,dy,0)</math>

Now we can compute the absolute value of the cross product between <math>\mathbf{\hat r}</math> and <math>d\mathbf{L}</math>, where <math>r = \sqrt{y^2 + z^2}</math>:

::<math>|d\mathbf{L} \times \mathbf{\hat r}| = \left|\begin{vmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ 0 & -\frac{y}{r} & \frac{z}{r} \\ 0 & dy & 0 \end{vmatrix}\right| = \Biggr| \ \mathbf{i} \biggr[0 \times \left(- \frac{y}{r}\right) - \frac{z}{r} dy \biggr] - \mathbf{j} \biggr[0 - 0 \times \frac{z}{r} \biggr] + \mathbf{k} \biggr[0 \times dy - 0 \times \left(-\frac{y}{r}\right) \biggr] \ \Biggr| = \Biggr| \ \mathbf{i}\biggr[-\frac{z}{r}dy \biggr] - \mathbf{j}\biggr[0 \biggr] + \mathbf{k}\biggr[0 \biggr] \ \Biggr| = \Biggr| \ \left(-\frac{z}{r}dy,0,0\right) \ \Biggr| = \left(\frac{z}{r}dy, 0, 0\right)</math>

Thus we have:

::<math>d\mathbf{B} = \frac{\mu_{0}}{4\pi} \frac{I \left(\frac{z}{r}dy, 0, 0\right)}{r^2} = \frac{\mu_{0}}{4\pi} \frac{Iz}{r^3}dy = \frac{\mu_{0}}{4\pi} \frac{Iz}{(y^2 + z^2)^{3/2}}dy</math>

To find the total magnetic field at a point along the z-axis due to the wire, we integrate from one end of the wire to the other end of the wire, or in this case:

::<math>-\frac{L_0}{2}</math> to <math>\frac{L_{0}}{2}</math>, since the wire is centered at the origin and along the y-axis.

The integral then is:

::<math>\int d\mathbf{B} = \int_{-L_0/2}^{L_0/2} \frac{\mu_{0}}{4\pi} \frac{Iz}{(y^2 + z^2)^{3/2}}dy = \frac{\mu_0}{4\pi} \frac{IL}{z\sqrt{z^2 + (L/2)^2}}</math>

Therefore, the total magnetic field <math>B</math> due to a wire of length <math> L </math> with current <math> I </math> at a distance <math> z </math> away from the wire is:

::<math>B = \frac{\mu_0}{4\pi} \frac{IL}{z\sqrt{z^2 + (L/2)^2}}</math>

====Approximation====

If it is known that <math>L >> z</math>, then the denominator of the above formula can be approximated by:

::<math> \sqrt{z^2+(L/2)^2} \approx \frac{L}{2} </math>

Therefore, if you have a really long wire, and you are trying to find the magnetic field of a point relatively close to the rod, you can use the approximation:

::<math> B = \frac{\mu_0}{2\pi} \frac{I}{z} </math> [1]

In most situations, at least in the scope of this course, it is stated in the question whether or not you can use the approximation. This can come in a few different forms: "assume z<<L," "assume the length of the wire is much longer than than the distance from the wire to the observation location," etc. However, if it is not explicitly stated, a good rule of thumb is that if the length of the wire is 100 times+ the <math>z</math>, we can use the approximation formula. Otherwise, it is smart to just play it safe and use the full formula.

==GlowScript Code Example: Wire Interaction==

mu0 = 4 * pi * 1e-7
wire1 = cylinder(pos=vec(0,0,-5), axis=vec(0,0,10), radius=0.05, color=color.red)
I1 = 5
radii = [0.5, 1.0, 1.5]
for r in radii:
for theta in arange(0, 2*pi, pi/12):
x = r*cos(theta)
y = r*sin(theta)
B_dir = cross(vec(x, y, 0), vec(0, 0, 1))
B_dir = B_dir.norm()
arrow(pos=vec(x, y, 0), axis=0.2*B_dir, color=color.blue)
label(pos=vec(0,2,0), text="Magnetic Field around Wire 1", box=False, height=10, color=color.black)
r_point = vec(0, 1, 0)
B_mag = (mu0 / (2*pi)) * (I1 / mag(r_point))
B_vec = cross(r_point, vec(0,0,1)).norm() * B_mag
arrow(pos=r_point, axis=0.2*B_vec.norm(), color=color.green)
label(pos=r_point + vec(0.2,0.2,0), text="B at this point", box=False, height=10, color=color.green)
wire2 = cylinder(pos=vec(1,0,-5), axis=vec(0,0,10), radius=0.05, color=color.orange)
I2 = 5
r = mag(wire2.pos - wire1.pos)
F_per_L = (mu0 / (2*pi)) * I1 * I2 / r
direction = vec(1,0,0) if I1*I2 < 0 else vec(-1,0,0)
arrow(pos=wire2.pos + vec(0,0,5), axis=0.2*direction, color=color.magenta)
label(pos=wire2.pos + vec(0.2,0,5), text="Force on Wire 2", box=False, height=10, color=color.magenta)

==Magnetic Field Near a Midpoint of the Wire==
===Computational Model===
This can be found in the mathematical model section where the infinitesimal piece is integrated.
This can also be done in Glowscript as shown below:

:d = display(height=400, width=1000)
:d.background = color.white
:d.forward = vector(-0.2, -0.2, -1)

:L = 1
:d.range = 0.2 * L
:d.center = vector(0.15 * L, 0, 0)

:I = 5
:kmag = 1e-7
:N = 20
:dx = L / N
:dl = vector(dx, 0, 0)

:wire = []
:for x in arange(-L/2, L/2, dx):
c = cylinder(pos=vector(x, 0, 0), axis=dl * 0.9, radius=0.005, color=color.orange)
wire.append(c)

:arr = []
:da = L/8
:for x in arange(-L/2+2*da, L/2-da, da):
:::for theta in arange(0, 2*pi, pi/4):
:::b = arrow(pos=vector(x,-r1*sin(theta), r1*cos(theta)), color=color.cyan,
::::::shaftwidth = 0.008, axis=vector(0,0,0))
:::arr.append(b)
:for x in arange(-L/2+2*da, L/2-da, da):
:::for theta in arange(0, 2*pi, pi/4):
::::::b = arrow(pos=vector(x,-r2*sin(theta), r2*cos(theta)), color=color.cyan,
:::::::::shaftwidth = 0.004, axis=vector(0,0,0))
::::::arr.append(b)
:ra = arrow(pos=vector(0,0,0), axis=vector(0,0,0), color=color.red, shaftwidth=0.005)
:dla = arrow(pos=vector(0,0,0), axis=vector(0,0,0), color=color.magenta, shaftwidth=0.005)
:dl_label = label(pos=dla.pos, text="dl", yoffset=8, xoffset=3, color=dla.color, opacity=0, box=0, line=0, height=24)
:r_label = label(pos = ra.pos + ra.axis/2, color=ra.color, text="r", yoffset=-7, xoffset=5, opacity=0, box=0, line=0, height=24)

:count = 0
:rateval = 200
:for a in arr:
:::for s in wire:
::::::rate(rateval)
::::::r = a.pos - (s.pos+dl/2)
::::::ra.pos = (s.pos+dl/2)
::::::ra.axis = r
::::::r_label.pos = ra.pos + ra.axis/2
::::::dla.pos = s.pos+vector(0,0.011,0)
::::::dla.axis = dl
::::::dl_label.pos = dla.pos
::::::a.axis = a.axis +Bscale*kmag*I*cross(dl, norm(r))/mag(r)**2
::::::if count < 20:
:::::::::d.waitfor('click')
::::::elif count < 2*N:
:::::::::rateval = 2
::::::elif count < 8*N:
:::::::::rateval = 5
::::::elif count < 40*N:
:::::::::rateval = 50
::::::else:
:::::::::rateval = 100
::::::count = count+1

:ra.visible = False
:dla.visible = False
:r_label.visible = False
:dl_label.visible = False

====Application with a Compass====

If you run a current through a wire and place a compass near it, the needle of the compass deflects due to the magnetic field from this wire. With no current in the wire, the compass will face North. When approximately .314A is run through a wire, the compass deflects by approximately 20 degrees. In fact, the amount of deflection that there is from the wire can actually help you calculate the approximate magnetic field of the wire. This is because there is a particular relationship between the needle of the compass, the magnetic field of the wire, and the magnetic field of the Earth itself that looks like this:

::<math> |B_w| = |B_E| \text{tan}\theta </math>

The Earth itself has a magnetic field anywhere on the Earth (based on location it varies slightly, but it is easier to assume it is constant) of approximately <math>2e^{-5} \ \text{T}</math> which is why the compass points notes. In the formula above, theta is the amount of degrees that, when placed directly above or underneath, the compass needle deflects from North. This is a very useful formula to have in lab or in the real world if it is unknown how much current is running through a wire.

==Examples==
===Easy===

The magnitude of the magnetic field <math>50 \ \text{cm}</math> from a long, thin, straight wire is<math> 8.0 \ \text{μT}</math>.

:'''a) What is the approximate current through the long wire?'''

::Using the approximation formula for a long, thin straight wire,

:::<math>B = \frac{\mu_{0}}{4\pi}\frac{2I}{r}</math>

::we see the current needed to supply the stated magnetic field is:

:::<math>I = \frac{4\pi r B}{2 \mu_{0}} = \frac{4\pi \times 0.5 \times 8.0 \times 10^{-6}}{2 \times 4\pi \times 10^{-7}} = 20 \ \text{A}</math>

:'''b) An ordinary compass that points north when not in the vicinity of a magnetic field is pointing at <math>\theta_{1} = 325^{°}</math>. A wire with a current is then placed directly above the compass and the needle now points at <math>\theta_{2} = 240^{°}</math>. What is the approximate magnitude of the magnetic field of this wire?'''

::Using our useful lab formula:

:::<math> |B_{wire}| = |B_E| \text{tan}(\theta)</math>

::<math>\theta</math> will equal the difference between the initial angle and the final angle:

:::<math>\theta = \theta_{2} - \theta_{1} = 240 - 325 = -85° </math>

::Therefore:

:::<math>|B_w| = 2e^{-5} \times \text{tan}(-85°)</math>

:::<math>|B_w| = 2.29 \times 10^{-4} \ \text{T} </math>

===Medium===

The current through a thin, straight wire that is <math>2 \ \text{m}</math> long is <math>74 \ \text{A}</math>.

:'''a) What is the magnitude of the magnetic field at a location <math>0.35 \ \text{m}</math> away and perpendicular to the center of the wire?'''

::Using the full formula:

:::<math> B = \frac{\mu_0}{4\pi} \frac{LI}{z\sqrt{z^2+(L/2)^2}} </math>

:::<math> B = \frac{\mu_0}{4\pi} \frac{2 \times 74}{0.35\sqrt{0.35^2+(2/2)^2}} </math>

:::<math> B = 39.912 \ \mu \text{T}</math>

===Difficult===

There are two wires, separated by a distance of <math>80</math> meters on the x-axis. The left wire has a current running through it of <math>5 \ \text{A}</math>, while the right wire has a current running through it of <math>12 \ \text{A}</math>. The length of the left wire is <math>2</math> meters, while the length of the right wire is <math>3</math> meters.

:'''a) Find the total magnetic field at a point on the x-axis directly in between the two wires.'''

::Using the full formula, the magnetic field due to the left wire is:

:::<math> B_L = \frac{\mu_0}{4\pi} \frac{LI}{z\sqrt{z^2+(L/2)^2}} </math>

:::<math> B_L = \frac{\mu_0}{4\pi} \frac{2 \times 5}{40\sqrt{40^2+(2/2)^2}} </math>

:::<math> B_L = 6.25 \times 10^{-10} \ \text{T}</math>

::The magnetic field due to the right wire then is:

:::<math> B_R = \frac{\mu_0}{4\pi} \frac{LI}{z\sqrt{z^2+(L/2)^2}} </math>

:::<math> B_R = \frac{\mu_0}{4\pi} \frac{3 \times 12}{-40\sqrt{(-40)^2+(3/2)^2}} </math>

:::<math> B_R = -2.25 \times 10^{-9} \ \text{T}</math>

::The total magnetic field will be the sum of the two magnetic fields:

:::<math> B_T = B_L + B_R </math>

:::<math> B_T = 6.25 \times 10^{-10} - 2.25 \times 10^{-9} </math>

:::<math> B_T = -1.62 \times 10^{-9} \ \text{T}</math>

==Connectedness==
I am very interested in clean energy storage and production, which typically involves long wires at some point between where the energy is generated and where the electricity is used. It is important to understand all the forces involved with an electrical current, so that if something goes wrong, you can determine where the problem is and why it might be occurring so that you can fix it.

I am an Electrical Engineering major, so all of the material within this class is vastly important, not only for the following courses required for an EE major, but also for the field once we graduate and find a job. However, this concept specifically interests me because for a while I had a very difficult time finding the direction of the magnetic field in situations such as these, so this is my way of giving back in an effort to make sure future students don't run into the same problem.

I am an Industrial Engineering major and think that it is really interesting to see the theory behind how compasses are affected by currents within a wire and their associated magnetism. A compass is such an everyday item but I had never looked into why it works the way it does, and this specific topic gave me a lot of insight into that. Additionally, it is really intriguing to learn about the second form of the right hand rule and its applications.

==See also==

===Further Reading===
*[http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/Biosav.html HyperPhysics Biot-Savart Law]<br>
*[https://www.youtube.com/watch?v=nfSJ62mzKyY Bozeman Science Magnetic Field of a Wire]<br>
*[https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Map%3A_University_Physics_II_-_Thermodynamics%2C_Electricity%2C_and_Magnetism_(OpenStax)/12%3A_Sources_of_Magnetic_Fields/12.2%3A_Magnetic_Field_due_to_a_Thin_Straight_Wire]<br>
*[https://projects.ncsu.edu/PER/Articles/LunkBFieldArticle.pdf]<br>

===External Links===
*[[Magnetic Field of a Loop]]<br>
*[[Magnetic Field of a Disk]]<br>
*[[Biot-Savart Law for Currents]]<br>
*[[Magnetic Field]]<br>
*[[Moving Point Charge]]<br>

==References==
*Matter and Interactions Vol. II

*OpenStax University Physics

*Skulls in the Stars