# Electromagnetism Definition and 341 Discussions

Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force is carried by electromagnetic fields composed of electric fields and magnetic fields, and it is responsible for electromagnetic radiation such as light. It is one of the four fundamental interactions (commonly called forces) in nature, together with the strong interaction, the weak interaction, and gravitation. At high energy, the weak force and electromagnetic force are unified as a single electroweak force.

Electromagnetic phenomena are defined in terms of the electromagnetic force, sometimes called the Lorentz force, which includes both electricity and magnetism as different manifestations of the same phenomenon. The electromagnetic force plays a major role in determining the internal properties of most objects encountered in daily life. The electromagnetic attraction between atomic nuclei and their orbital electrons holds atoms together. Electromagnetic forces are responsible for the chemical bonds between atoms which create molecules, and intermolecular forces. The electromagnetic force governs all chemical processes, which arise from interactions between the electrons of neighboring atoms. Electromagnetism is very widely used in modern technology, and electromagnetic theory is the basis of electric power engineering and electronics including digital technology.
There are numerous mathematical descriptions of the electromagnetic field. Most prominently, Maxwell's equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents.
The theoretical implications of electromagnetism, particularly the establishment of the speed of light based on properties of the "medium" of propagation (permeability and permittivity), led to the development of special relativity by Albert Einstein in 1905.

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1. ### Magnetic- and Electric- field lines due to a moving magnetic monopole

Question: My answer: What it looks like for an electric charge: Am I correct? If you want I can hand out my Latex on how I got to it, it will refer to the book Griffiths a lot.
2. ### Electric and magnetic fields of a moving charge

Part a) My solution: Big R basically becomes r, and the electric and magnetic field lines are doubled because of superposition principle. Am I right?
3. G

### Power dissipated by a resistor on a coaxial cable

I need help with part c. My solution: Is there an other way to do this other than dimensional analysis? P.S "dr an infinitesimal radius", it ofcourse should be dz.
4. ### MIT OCW, 8.02, Electromagnetism: Charged Cylindrical Shell

Here is figure 2.16.6 Here is the picture I drew to set up the problem My first question is if the reasoning and integrals are correct. I used Maple to compute the three integrals. The first two result in 0, which makes sense by symmetry. Maple can't seem to solve the last integral.
5. ### Two charged spheres hitting each other

Since the forces involved (gravity and electric force) are conservative we can use conservation of energy. The initial energy is ##E_i= k\frac{q_1q_2}{r_0}-G\frac{m^2}{r_0} ## and the final ##E_f=mv^2+k\frac{q_1q_2}{2r}-G\frac{m^2}{2r} ## so from ##E_i=E_f ## we get...
6. ### Hall effect over a conducting ring

This is the diagram provided in the question: The ring is made of conducting material. I was originally asked to find the potential difference between ##a## and ##b##. I did so using the Hall effect (and assuming it would work as per normal in this situation). This got me ##\Delta V = vBl##...
7. ### Radiation emitted by a decelerated particle

Honestly, folks, I don't even know how to start. I included in the Relevant Equations section the relativistic generalization of the Larmor formula according to Jackson, because that's the equation for the power emitted by an accelerated particle, but I don't see how that gets me very far. The...
8. ### I Can trains use permanent magnets to be propelled?

Can a train (e.g. like a maglev train) use a set of permanent magnets (not electromagnets) that somehow can be propelled and maintain at least a constant speed with them? Is this an example of such system...
9. ### I Query on Electromagnetic Theory (Dielectric Boundary Conditions)

The given question from Electromagnetic Theory (which is based on Dielectric Boundary Conditions) is as follows: Interface b/w two dielectric medium has a surface charge density (suppose xyz C / (m ^ 2) ). Using boundary condition find field in 1 (relative permittivity =xyz) if field in 2...
10. ### Conducting rod in equilibrium due to magnetic force

I am having problems understanding point (b) so I would like to know if my reasoning in that part is correct and/or how to think about that part because I don't see how to justify the assumption ##v_y=0\ m/s##. Thanks. I set up the ##xyz## coordinates system in the usual way with ##xy## in the...
11. ### Current through ring in solenoid-ring system

The following is my solution to this problem; I would appreciate some feedback, especially on part (b), which I have found the most challenging. Thanks. (a) Using Ampere's Law I get ##B=\mu_0 n i_1## where ##i_1## is the current through the solenoid, and since ##\phi=Li_1##, where ##L## is the...
12. ### I Magnetic field strength of a stack of magnets

I know that for a single cylindrical neodymium magnet, the formula $$\displaystyle{\displaylines{B(z)=\frac{μ_0M}{2}(\frac{z}{\sqrt{z^{2}+R^{2}}}-\frac{z-L}{\sqrt{(z-L)^{2}-R^{2}}})}}$$ shows the relationship between the magnetic field strength and the distance between the magnet. I was...
13. ### I Electric Field & Interplay between Coordinate Systems | DJ Griffiths

Hi. I believe I have what may be both a silly and or a weird query. In many Griffiths Problems based on Electric Field I have seen that a coordinate system other than Cartesian is being used; then using Cartesian the symmetry of the problem is worked out to deduce that the field is in (say) z...
14. ### I How an induced electric dipole vibrates with EM field

If we have an electromagnetic wave like the one in the picture and a molecule which is, in the image, the small black ball with electron cloud being the part with "minus sign" in it, does the molecule with its cloud start to oscillate, once the EM wave hits it, as an induced electric dipole...
15. ### Maximum charge on the plates of a capacitor

What I have done: The electromotive force due to Faraday's Law is: ##\mathcal{E}=-\frac{d\phi(\vec{B})}{dt}=\frac{d}{dt}(Ba^2)=a^2\frac{dB}{dt}=-10^{-4}V.## In the circuit, going around the loop in a clockwise fashion: ##\oint_{\Gamma}\vec{E}\cdot d\vec{l}=-\frac{d\phi(\vec{B})}{dt}\Rightarrow...
16. ### Relativistic particle in uniform magnetic field (solution check)

My solution was as follows: $$\frac {d\overrightarrow p} {dt}=q \frac {\overrightarrow v} {c}\times \overrightarrow B_0$$ The movement is in the ##[yz]## plane so ##|\overrightarrow v\times \overrightarrow B_0|=vB_0##, therefore: $$\biggr |\frac {dp} {dt}\biggr |= \frac {qvB_0} {c}.$$ On the...
17. ### Force to apply to a loop moving away from a current-carrying wire

What I have done: (1) ##\Phi(\vec{B})=\int_{S}\vec{B}\cdot d\vec{S}=-\frac{N\mu_0 il}{2\pi}\int_{s=h}^{s=h+l}\frac{ds}{s}=-\frac{\mu_0iNl}{2\pi}\ln(\frac{h+l}{h})## so ##\mathcal{E}=-\frac{d\phi(\vec{B})}{dt}=-\frac{\mu_0iNl^2v}{2\pi h(h+l)}## so...
18. ### Time for current in solenoid to be 10% less than the steady state current

I set up the equation ##V-iR-L\frac{di}{dt}=0##, with ##i(0)## and by solving it I got ##i(t)=\frac{V}{R}(1-e^{-\frac{R}{L}t})##. Then, since the steady state current is ##i_s=\frac{V}{R}## I imposed the condition ##i(t_1)=\frac{9}{10}\frac{V}{R}\Leftrightarrow...
19. ### Find the time for the current to fall to 35mA in this simple RL circuit

What I have done: (1) ##I(0)=\frac{V}{R}=\frac{1.5}{25}A=0.06 A.## (2) By setting ##I(t*)=0.06(1-e^{-(35/0.4)t*})=35 mA## we get ##t*\approx 0.01 s## What I have done seems correct to me, but the result for part (2) should be different. I would be grateful if someone could point out to me...
20. ### Flux of constant magnetic field through lateral surface of cylinder

If the question had been asking about the flux through the whole surface of the cylinder I would have said that the flux is 0, but since it is asking only about the lateral surfaces I am wondering how one could calculate such a flux not knowing how the cylinder is oriented in space. One could...
21. ### Three spherical conductors

(a) Using Gauss's Law ##E_P=\frac{q_1+q_2+q_3}{4\pi\varepsilon_0(R_1+R_2+R_3+d)^2}; (b) V_3-V_1=\int_{R_3}^{R_2}\frac{q_1+q_2}{4\pi\varepsilon_0 r^2}dr+\int_{R_2}^{R_1}\frac{q_1}{4\pi\varepsilon_0 r^2}dr=\frac{q_2}{4\pi\varepsilon_0}\left(\frac{1}{R_3}-\frac{1}{R_2}\right).## (c)...
22. ### Conducting cable surrounded by two cylindrical shells

What I have done: (a) If we start at ##R_5## then we have ##\Delta V=-\int_{R_5}^{R_1}\vec{E}\cdot d\vec{l}=-(\int_{R_5}^{R_4}\vec{0}\cdot d\vec{l}+\int_{R_4}^{R_3}\frac{\lambda}{\varepsilon_0}dl+\int_{R_3}^{R_2}\vec{0}\cdot d\vec{l}+\int_{R_2}^{R_1}\frac{\lambda}{\varepsilon_0}dl=-\lambda(...
23. ### B Do materials surrounding magnets affect how superconductors levitate?

I'm currently doing an experiment with magnetic levitation but I don't know if my independent variable will even affect my results at all. I am planning on building a rail of magnets and levitating a type 2 superconductor on it. I wanted to change the material surrounding the rail of magnets...
24. ### A Calculation of EM fields induced by an antenna in the near field

The title pretty much covers it. I'm having to calculate the field induced inside the human body by an antenna in the near field (essentially, a phone placed close to a user's head), and I'm drawing a blank on how to relate the field generated by the antenna to the field induced inside the...
25. ### I What makes a plasma collisionless?

Hi, I'm trying to understand what determines whether a plasma will be collisionless or collisional. I understand that a diffuse plasma with large mean free path will be collisionless but I don't really understand it from an electromagnetic point of view
26. ### Flux of the electric field that crosses the faces of a cube

a) $$\phi_T=\phi_F-\phi_I=10^4\cdot 4\cdot 4-10^4\cdot 4\cdot 4=0\, \textrm{Nm}^2/\textrm{C}$$ b) $$\phi_F=\underbrace{300\cdot 4}_{\vec{E}}\cdot \underbrace{4\cdot 4}_{\textrm{area}}=19200\, \textrm{Nm}^2/\textrm{C}$$ $$\phi_0 = 300\cdot 0\cdot 4\cdot 4=0\, \textrm{Nm}^2/\textrm{C}$$ Then...
27. ### Work to bring a charge to the center of two quarter circles

By measuring angle \theta from the positive ##x## axis counterclockwise as usual, I get ##d\vec{E}=k( (\lambda_2-\lambda_1)\cos(\theta)d\theta, (\lambda_2-\lambda_1)\sin(\theta)d\theta )## and by integrating from ##\theta=0## to ##\theta=\frac{\pi}{2}## I get...
28. ### An iron cylinder inside a solenoid

From ##\oint_{\Gamma}\vec{H}\cdot d\vec{l}=\sum I## by Ampere's Law which gives ##H \Delta l=\Delta N\cdot i\Leftrightarrow H=n i## where ##n=## number of turns per unit length so ##i=\frac{H}{n}=\frac{10^3 A / m}{\frac{200}{0.2m}}=1 A##. Since ##\vec{H}=\frac{\vec{B}-\mu_0\vec{M}}{\mu_0}## we...
29. ### A disconnected capacitor with two dielectrics in parallel

I considered the capacitor as two capacitors in parallel, so the total capacitance is ##C=C_1+C_2=\frac{\varepsilon_0\varepsilon_1 (A/2)}{d}+\frac{\varepsilon_0\varepsilon_2 (A/2)}{d}=\frac{\varepsilon_0 A}{2d}(\varepsilon_1+\varepsilon_2).## Since the parallel component of the electric field...
30. ### I Measuring characteristic impedance as suggested by KRAUS' book

Can someone provide more information about this method to measure chracteristic impedance using resistance paper?. Kraus' book claims that the characteristic impedance can be measured by simple dc measurement. It even shows a case to mesure the impedance of a coaxial cable with square outer...
31. ### Magnetization of ferromagnetic material

I have thought about the following ##\oint \vec{H}\cdot d\vec{l}=0\Leftrightarrow H_{int}(D-h)+H_{ext}h=0\Leftrightarrow (\frac{B}{\mu_0}-M)(D-h)+\frac{B}{\mu_0}h=0\Leftrightarrow M=\frac{D}{D-h}\frac{B}{\mu_0}## but (supposing what I have done is correct) I don't understand which value of ##B##...
32. ### Magnetic working point

From the graph we see that at ##H=4 kA/m,\ B=1.5T##. We have that ##M=\frac{B}{\mu_0}-H=\frac{1.5T}{\mu_0}-4kA/m## and from Ampere's Law that ##i=\frac{HL}{N}=\frac{4kA/m\cdot 0.1 m}{100}## and the current (density on the surface is) ##\sigma_{m}=M##. Does this make sense? I am having...
33. ### Mean energy density of solar radiation and magnitude of Poynting vector

I have doubts about the wording of the exercise: (1) energy density is ##u=\varepsilon_0 (cB)^2## but since the question asks for mean energy density should I perhaps average over ##cos^2 (\omega t)## (there due to the ##B^2##) and thus use ##<u>=\frac{1}{2}\varepsilon_0 (cB)^2##? (2) it seems...
34. ### Potential due to a finite charged wire

Considering a reference frame with ##x=0## at the leftmost point I have for the leftmost piece of wire: ##\int_{x=0}^{x=2R}\frac{\lambda dx}{4\pi\varepsilon_0 (3R-x)}=\frac{\lambda ln(3)}{4\pi\varepsilon_0}##. The potential at O due to the semicircular piece of wire at the center is...
35. ### Maximum charge on a spherical capacitor

The electric field is the one generated by the charge ##+Q## on the inner sphere of the capacitor, which generates a radial electric field ##\vec{E}=\frac{1}{4\pi\varepsilon_0}\frac{Q}{r^2}\hat{r}## which, due to the presence of the dielectric, become...
36. ### I Guidance Requested on Inductance Formula for Solenoid

In my textbook on EM, the formula for self inductance of a finite solenoid is given as: L= (μ(o)* N^2*A * {√(a^2+ l^2) - a} )/l^2 where a=Radius of each turn, l=length of solenoid. I am having trouble and extreme difficulty in trying to ascertain how this formula was derived in the book and...
37. ### Trajectory of an electron traveling near a current-carrying wire

B equals 50*10^-7 T (at first instance) Fm equals 8*10^-20 N (at first instance) I know Fm is perpendicular to the velocity, and I know the estimation of the trajectory (somewhat similar to the curve y=lnx). Since I think vertical velocity will be constant, only changing the x component, I...
38. ### I EM Power transmitted from one region to another (normal incidence)

High! I have a EM plane wave hitting normally a surface dividing universe in media 1 and 2, both without losses. So we have incident, reflected and transmitted waves. It's a simple exercise in which you are given the basic data about two media and wave incident amplitude H in medium 1. I get...
39. ### Understanding the electric force felt by the charges on a sphere

A thin shell in reality doesn't have zero thickness. Consider the image below, showing a cross-section of a small portion of the shell: Here we are considering a more general case in which we have electric fields of magnitude ##E_1## and ##E_2## on each side of the shell. Gauss's Law...

41. ### I Energy Flow From Battery to the Light Bulb

When we connect tungsten filament light bulb to the battery, filament becomes hot due to electrons losing kinetic energy in the electric field inside of conductor. Heat is eventually converted to electromagnetic radiation making light bulb shine. Light energy comes from flow of electrons and...
42. ### On which objects can we apply Gauss' Law to find the electric field?

What am I missing? I also don't get the title of the section: "Charge distributions with enough symmetry for Gauss's Law". I thought Gauss's Law was valid for any closed surface enclosing a charge. I don't understand what "enough symmetry" means in the title above. I get that with symmetry...
43. ### Electric field is constant around charged infinite plane. Why?

Using Gauss's Law By using a symmetry argument, we expect the magnitude of the electric field to be constant on planes parallel to the non-conducting plane. We need to choose a Gaussian surface. A straightforward one is a cylinder, ie a "Gaussian pillbox". The charge enclosed is...
44. ### Solenoid gap magnetic field

Hey, I was trying to figure out this problem. I got (a) using B = mu * NI/L but I'm not sure how to start the part about the magnetic field in the gap after the solenoid is ripped in half with 1 cm gap. Thanks for the help!
45. ### Calculate the electric field due to a charged disk (how to do the integration?)

I am interested in particular in the second integral, in the ##\hat{r}## direction. Here is my depiction of the problem: As far as I can tell, due to the symmetry of the problem, this integral should be zero. $$\int_0^R \frac{r^2}{(x^2+r^2)^{3/2}}dr\hat{r}$$ I don't believe I need to...
46. ### Electric field created by two charged circular arcs?

The strategy will be to figure out what ##dq##, ##\hat{r}_{dq,p}##, and ##r_{dq,p}## are, plug them into the expression for ##d\vec{E}_{p_r}##, then integrate over ##d\vec{E}_{p_r}## to obtain ##\vec{E}_{p_r}##, the electric field at ##P## due to the arc on the right. Then I will repeat the...
47. ### How to choose the correct function to use for a Taylor expansion?

Consider two different Taylor expansions. First, let ##f_1(s)=(1+s)^{1/2}## $$f_1'(s)=-\frac{1}{2(1+s^{3/2})}$$ Near ##s=0##, we have the first order Taylor expansion $$f_1(s) \approx 1 - \frac{s}{2}$$ Now consider a different choice for ##f(s)## $$f_2(s)=(1+s^2)^{1/2}$$...
48. ### MIT OCW 8.02 Electromagnetism: how were these two limits calculated?

I know what the answers are, because this is all part of the notes from MIT OCW's 8.02 Electromagnetism course. In case you want to see the actual problem, it is example 2.3 that starts on page 18; the limits I am asking about are on page 20. How do I go about calculating the limits? Ie, what...
49. ### I How do photons transfer energy?

Hi! So I know about the electron-photon interaction but what about photon-photon interaction? I mean, I do know there is a very small chance for them to interact, but how else do they transfer energy in order to get from Sun to Earth, for example? When it comes to sound waves I get it, for...
50. ### I Gauge in the Aharonov Bohm effect

In p.385 of Griffiths QM the vector potential ##\textbf{A} = \frac{\Phi}{2\pi r}\hat{\phi}## is chosen for the region outside a long solenoid. However, couldn't we also have chosen a vector potential that is a multiple of this, namely ##\textbf{A} = \alpha \frac{\Phi}{2\pi r} \hat{\phi}## where...