Field Definition and 1000 Threads

1) Why is the electric field 0 at the bottom of Gaussian surface? Isn't the electric field on both sides of the surface, pointing down and outwards like a plane of charge? see image. 2) Why does a charge distribution with cylindrical symmetry have to be infinitely long? 3) My book says a...

I want to improve the magnetic field strength at the surface of a magnet configuration by utilizing diamagnetic materials to guide the magnetic field lines. I have not the proper equipment to measure the effect myself but would this work? This is the initial configuration with four magnets side...

The solution says that the tension in the string in the negative x direction is balanced by the force of the plate on the ball (red). Why is the repulsive force of the ball on the plate (in blue) not included in this calculation?

Does the electric field vector takes into account the field's radial direction? Usually when we calculate the electric field, we use ##\vec E = \frac{kq}{r^2}\vec j##, which is a straight line vector of a positive charge q's electric field. This electric field points from a positive charge q to...

What I don't understand is how come the electric field of the negative plane isn't pointing towards the positive plane (in blue) and cancelling out the electric field of the positive plane (in red). See image

Suppose a molecule from our surrounding air (at ambient temperature) is being selected and is ionized. By some mechanical means, some velocity (say 100 m/s) is added to it and it has been put into a magnetic field perpendicular to its direction of motion. We all know how the molecule will behave...

Does a body accelerating at 1g in outer space create a gravitational field around it ?

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...

hello, 1. according to Robert Wald, General Relativity, equation (4.2.22) the magnetic field as measured by an observer with 4-velocity ## v^b ## is given by ## B_a = - \frac {1}{2} {ϵ_{ab}}^{cd} F_{cd} v^b ## where ## {ϵ_{ab}}^{cd}##, the author says, is the totally antisymmetric tensor (for...

since the cosmological constant observed is that there is a small amount of energy in empty space, and in general relativity anytime there is energy there is curvature and therefore gravity, how to calculate gravitational field with dark energy and does it have any observable effects on matter...

ρ_kdk = k^2/π^2 dk is the density of field modes (what we are trying to solve for here), and as ρ_kdk = ρ_λdλ, and k=2π/λ, we can rearrange this to get ρ_λdλ = 8π/λ^4dλ This is where my confusion lies. I am not sure what to do next. I know this equation physically means the number of modes per...

Hello everybody, I was visualizing the electric field radiation pattern of an antenna in a 3D EM simulation software (CST), and to see it with my eyes made me realize something I probably heard during my studies but forgot. What is the phenomenon behind what you can see below, which is the...

I'm probably inadequately equipped to understand this paper by Bucholtz, Longo and Rehren on "Causal Lie products of free fields and the emergence of quantum field theory", but I decided to give it a try. Alas, I got stuck in the 1st para of sect 2 where it says: Although I've seen the term...

Hello there, for the above problem the wavefunctions can be shown to be: $$\psi_{n,l}=\left[ \frac {b}{2\pi l_b^2} \frac{n!}{2^l(n+l)!}\right]^{\frac12} \exp{(-il\theta - \frac {r^2\sqrt{b}}{4l_b^2})} \left( \frac {r\sqrt{b}}{l_b}\right)^lL_n^l(\frac {r^2b}{4l_b^2})$$ Here ##b = \sqrt{1 +...

I am stuck deriving the gauge field produced in curved spacetime for a complex scalar field. If the underlying spacetime changes, I would assume it would change the normal Lagrangian and the gauge field in the same way, so at first guess I would say the gauge field remains unchanged. If there...

In quantum field theory, we have the following expansion on a scalar field (I follow the convention of Schwarz's book) $$\phi(\vec{x},t)=\int d^3 p \frac{a_p exp(-ip_\mu x^\mu)+a_p^{\dagger}exp(ip_\mu x^\mu)}{(2\pi)^3 \sqrt{2\omega_p}} \quad p^{\mu}=(\omega_p,\vec{p})$$ With commutation relation...

1)Field Lines is supposed to represent the electric field around a charge ,now we can draw infinite field lines around a charge and sinc Electric flux is No of Field Lines /area ,does it become infinite ,the whole concept of field lines is quite in the Gray Area for me ,I can in theory mark...

3 cm is inside the cylinder. We can use a gaussian cylinder to enclose the inside of the cylinder up to 3 cm. Because the outer cylinder is infinite there is no flux out of the end caps with the inner cylinder. There is also no charge enclosed in the cylinder. So the electric field 3cm away from...

If I have a point charge q right outside of a gaussian surface, it makes sense that the flux is zero inside the surface because the electric field going in equals the electric field going out. However, how would the electric field be zero inside? Wouldn't it just take on the electric field of...

At point ##P(0,0'03,0'04)## the field caused by the sphere is added to the field caused by the plane. First, ##E_\sigma## $$E_\sigma=\dfrac{\sigma}{2\varepsilon_0}=\dfrac{0,2\cdot 10^{-6}}{2\varepsilon_0}=11299,44\, \textrm{V}/\textrm{m}$$ Then, ##E_0##: Because ##r<R##...

Hello there, i wanted to ask if anyone knows a process or mechanism, that reduces the electric field that is requiered to tunnel an electron. When i use the work function of 4 eV (Aluminum) i get with Schottky-Nordheim approach a field of 870 kV/mm to tunnel an electron. Measurements tho just...

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...

I have the calculation of the electric field created by a ring of radius ##R## uniformly charged with a linear density of charge ##\lambda## at any point on the axis perpendicular to its surface (##z## axis), but I have some doubts about it. I'll leave you the calculation done first: In ##x##...

Draw a Gaussian pill box that starts from 0 (half way between the slab) and extends towards 2 cm.$$A \times \int_{0}^{0.02} \rho dz$$ I'm not sure if I should multiply the integral by A (area) or V (volume) And if area would I multiply by 0.02^2? I'm confused here. Thanks for your help.

Hey, I have a really short question about electrostatics. The boundary conditions are : \mathbf{E}^{\perp }_{above} - \mathbf{E}^{\perp}_{below} = -\frac{\sigma}{\varepsilon_{0}}\mathbf{\hat{n}} , \mathbf{E}^{\parallel }_{above} = \mathbf{E}^{\parallel}_{below}. My question is what is...

What happens to the higgs field when say a fusion reaction occurs. Like if mass is converted into energy and the higgs field gives a particle mass what happens to higgs field. I doubt this, but is the higgs field the mechanism that converts mass into gamma rays. Go easy on me I only have a high...

I have to prove three equations above. For first two equations, I've been thought and made reasonable answer by using a definition of the electricfield. However, for third, I can't use a definition of a magnetic field due to the cross product Like J_2 X J_1 X (r_2 - r_1). I think three of 'em...

What's the best shape function/element in finite element methods for phase field simulation?

define charge at an infinitesimal length of arc $$dQ = \lambda R d \theta$$We only care about the x component of the electric field because the y components cancel due to symmetry $$dE_x = \frac{k_e dQ}{R^2} cos \theta$$ Integrate to add up the infinitesimal parts. A quarter circle means 90...

We know the net force on the charged particle in the uniform electric field pointing up is mg - qE. To get acceleration, divide the net force by mass to get g - qE/m Plug into kinematic equation and get velocity by itself and substitute$$\sqrt{h(2g - \frac{q \sigma}{\epsilon_o m})}$$

λ1 = 3 microC/m λ2= -4 microC/m __________ . __________ l----L1---l-a1-l-a2-l-----L2---l (Not to scale) L1 = length of rod 1 (1m) a1 = length of end of rod 1 to point (0.7m) L2 = length of rod 2 (1m) a2 = length of end of rod 2 to point (0.3m) k = e field constant...

To calculate the Hamiltonian of a charged particle immersed in an electromagnetic field, one calculates the Lagrangian with Euler's equation obtaining ##L=\frac{1}{2}mv^2-e\phi+e\vec{v}\cdot\vec{A}## where ##\phi## is the scalar potential and ##\vec{A}## the vector potential, and then we go to...

Hi there, In his book "Quantum field theory and the standard model", Schwartz assumes that the canonical commutation relations for a free scalar field also apply to interacting fields (page 79, section 7.1). As a justification he states: I do not understand this explanation. Can you please...

I don't understand why there is potential difference between point A and O. Is there any change in magnetic flux experienced by the ring? I think the magnetic field passing through the ring's cross sectional area is constant Thanks

Question: Equation: Attempt: Can someone verify my answer?

Hi ... How can I find the electric field due to a thin circular ring of radius a and charge q for points outside the plane of the ring? The distance from the center of the ring to the point of the electric field is large compared to the radius of the ring. I have answered it but I don't know if...

I'm having an exam soon so i want to make sure. Is the electric field here zero?? cause if i draw gauss surface covering both of them they should cancel out or am i wrong.

I know that inside region 1, the D-field is zero as it is a conducting sphere, the E-field must be zero. It makes sense that in region 2 (inside the dielectric) there is a D-field. My question is, is there a D-field outside the dielectric material (r>R)? Obviously there will be an E-field, but...

If a electrically charged mass travels thru a magnetic(m) field, it will accelerate at right angles to its velocity and the m-field. Under some conditions like this the charged mass will travel in a circular loop due to this magnetic force acceleration. This info is all over the internet. e.g...

I came across this upcoming book -- https://press.princeton.edu/books/hardcover/9780691174297/quantum-field-theory-as-simply-as-possible -- peer reviewed as it is published by Princeton University Press, which is due to be published in October. I've already ordered a copy coming from the UK. It...

I believe I have all parameters set up correctly to evaluate part A of this problem but I am unsure of the bounds. I can't integrate from 0 to R because that part of this sheet has a hole there. I need to integrate from R to the other end of the sheet. Im not sure how I would figure out the...

I wanted to post my work so far to see if I am on the right path toward the correct answer so far. I have attached a ss of the actual problem and my work in the attachments

Im having trouble understanding the wording to this problem. When it says "from r=0 to r=infinity". My Qenc would zero out. I guess it makes sense that from infinitely far away you wouldn't "feel' the electric field but considering this question leads to 4 other questions I don't think I am...

I am a research student of MS PHYSICS. I have to numerically solve Friedman equation coupled to scalar field(phi). It is given in research paper of Sean Carroll, Mark Trodden and Hoffman entitled as ""can the dark energy equation of state parameter w be less than-1?""...

I've calculated the intensity for every point charge which are EA = 6.741 x 10¹³ NC¯¹ EB = 4.494 x 10¹¹ NC¯¹ EC = 6.741 x 10¹³ NC¯¹ and I am pretty sure about this far but I am struggling to calculate the X-axis intensity and Y-axis intensity to find the entire approximate intensity with the...

The EM field seems to be required for for local gauge symmetry of the electron matter field under local phase variation. Following is a description (not my verbiage): There is a symmetry in physics which we might call the Local Phase Symmetry in quantum mechanics. In this symmetry we change...

The removed mass is ##\frac{1}{8}M## My idea is to find ##g## from large sphere then minus it with ##g## from small sphere (because of the removed mass): ##g## at A = $$\frac{GM}{R^3}\left(\frac{1}{2}R\right)-\frac{G\left(\frac{1}{8}M\right)}{R^2}$$ Is this correct? Thanks

I encountered a problem regarding the appropriate sign needed to be taken for the work done on a dipole when it rotates in a uniform electric field and would appreciate some help. The torque on a dipole can be defined as τ=PEsinθ The work done on a dipole to move it from an angle ##\theta_0##...

Greetings The exercice consist of calulating the circuitation of the Field F along a the borders of the region omega my problem was how they found that y goes from 0 to h ( for 0 it´s clear but the mystery for me is h) Thank you!

I want to wrap no. 16 copper wire around 1" copper pipe to create a mag field. At 120v / 1 amp AC, how many turns will I need to get about 5 milligauss near the pipe?