Field Definition and 1000 Threads

The problem is as above, My attempt is as below but there is lot of effort in terms of imagining and not very confident, Required the magnetic field on the y-axis let us say point P. The magnetic field due to the x-axis wire is out of the paper at P with the values as R=2.0m, i =30A. B1 =...

My attempt is the magnetic field due to loop1 and loop2 should get added The magnetic field due to loop1 is B1 =(μ0 * Φ * i)/(4*π*r) = (4*π*(2*π)*0.004) /(4 *π*0.015) = 1670nT. I assumed this value should be less than 100nT. What is the reason? The other question is "Loop 2 is to be rotated...

When introducing renormalization of fields, we define the "free Lagrangian" to be the kinetic and mass terms, using the renormalized fields. The remaining kinetic term is treated as an "interaction" counterterm. If we write down the Hamiltonian, the split between "free" and "interaction" terms...

How would you respond to postdoc applicants if they hold a PhD in another field (physical oceanography) and then complete an MRes in astrophysics? Just interested because I don't qualify for funding for any of the astronomy and cosmology PhD positions I'v found in the UK (even though I am...

Source: Principles of Nano-Optics, for Lukas Novotny and Bert Hecht.The equations above represent the electric field in the second medium when a light hit a surface and the condition of TIR (total internal reflection) is satisfied. Actually this is what called Evanescent field. The point is if I...

I am interested in showing a visualization of water molecules in a time-varying electric/magnetic field as part of my PhD work. I would like something like this visualization: , but with an external time-varying field applied. At first, I thought of simply animating water molecules...

The load system formed by the point load and the load distribution generates two regions in space corresponding to r<1m and r>1m, i.e. inside and outside the sphere. Given the symmetry of the distribution, by means of the Gaussian theorem we can find the modulus of the field at a distance r from...

Trying to better understand quantum field theory, I've read that particles are created when it becomes an exitation of its quantum field. Would it then be right to think of a particle as the manifested kinetic energy of its field?

Hi everyone! I have during my time here on PF have posted a number of threads related to employment demand for STEM majors, including the following back in 2017: https://www.physicsforums.com/threads/which-stem-field-could-be-the-most-employable-in-2017.898554/ I wanted to take the...

An old field theory notebook has given me a formula for a long straight conductor that H = I/2πd which suggests 2.3873T at 0.2mm. Is it a reasonable approximation to use this as a basis for selecting the sensor? Any help much appreciated.

Can anyone explain while calculating $$\left \{ \Psi, \Psi^\dagger \right \} $$, set of equation 5.4 in david tong notes lead us to $$Σ_s Σ_r [b_p^s u^s(p)e^{ipx} b_q^r†u^r†(q)e^{-iqy}+ b_q^r †u^r†(q)e^{-iqy} b_p^s u^s(p)e^{ipx}].$$ My question is how the above mentioned terms can be written as...

Note that the solution is 5625 V/m in z direction which is found easier using Gauss' law, but I want to find the same result using Coulombs law for confirmation. Lets give the radius 0.04 the variable a = 0.04m. ##\rho## is the charge distribution distributed evenly on the surface of the...

Based on the conditions, I found that $$V(x)=\frac{a^2}{\pi^2} ρ_0sin(πx/a)$$ would be a solution to Laplace's equation for $$|x|\leq a$$ and $$V(x)=cx+d$$, where c and d are constants. From the boundary conditions, $$\frac{dV(a)}{dx}=\frac{a}{\pi} ρ_0cos(πa/a)=ac$$, $$c=\frac{a\rho}{\pi}$$ and...

I am struggling to get my work to match the posted solutions to this problem. I understand part (a) but can’t get the integral to work out for (b). I know I have to use Biot-Savart and add up the components from the the surface and volume currents. The cylinder is very long, so I need to make a...

My attempt: I know from Gauss' law in dielectric ##\nabla .D = ρ_f## where ##D = ε_0E + P##, so as ##ρ_f = 0## (as there is no free charge in the sphere) => ##\nabla .D = 0## => ##ε_0\nabla .E = \nabla .P## from this I get ##E = \frac {-kr^2 \hat r} {ε_0}## But, I know that for a uniformly...

When the bar moves ,magnetic force is applied to all the charged particles.At the equilibrium the electric and magnetic force have the same value and the positive and negative charges are accumulated in the two sides of ab. Eq=qVB, E=VB Here is when cannot continue,I thought it like a capacitor...

I am trying to understand “divergence” by considering a one-dimensional example of the vector y defined by: . the parabola: y = -1 + x^2 The direction of the vector y will either be to the right ( R) when y is positive or to the Left (L). The gradient = dy/dx = Divergence = Div y = 2 x x...

I have a problem with the derivation above I don't get how Can someone derive this and illustrate this visually for example by using Figure 2 or using another drawing?

Assume that an infinite metallic plate A lies in the xy-plane, and another infinite metallic plate B is parallel to A and at height z = h. The potential of plate A is 0, and the potential of plate B is constant and equal to V. So, there is a uniform electrostatic field E between plates A and B...

This is not really homework, but I'm having trouble understanding it intuitively. I came across this when learning about the space charge layer of a diode. The solution I know simply uses the 1D form of Gauss's law: ##\vec{\nabla} \cdot \vec{E}## = ##\dfrac{\rho}{\epsilon_0}## becomes...

I first tried to use the Gauss' law equation E.A = q/ε0 to find the total charge enclosed. The answer came out to be q(enclosed) = 4πqε0e^(-4r). So for r approaching infinity, q(enclosed) approached 0. Next, I tried the equation ∇·E = ρ/ε0, calculated rho to be -4qε0e^(-4r)/r^2 and total...

I am pretty confused where to even start with this question, which is not a good thing less than a week before the final :(. One thing in particular that I don't get is that I thought we were using the Clebsch-Gordon coefficients for ##\vert jm \rangle ## states, not for ##\vert J, J_z \rangle...

Inner conductor radius = 1cm outer conductor radius = 10cm region between conductors has conductivity = 0 & 𝜇r = 100 𝜇r = 1 for inner and outer conductor Io = 1A(-az) 𝑱(𝑟) = (10^4)(𝑒^-(r/a)^2)(az) Problem has cylindrical symmetry, use cylindrical coordinate system. Find the total current...

The first time I saw this question I had no idea how to do it (as you can see in the figure, I lost a lot of points :s) because I was confused on how to even approach it with area of the slab from all sides being infinity. Right? That's problematic, no? Today, I just tried the problem again for...

I have some questions about this answer. Why do they use absolute value when writing in the limits in the integral underlined with orange? And how do they get from this value where I have underlined with orange to the answer for E outside the sphere. Can someone do the rewriting? And last why is...

For a infinitesimal wire of lengh dx, the induced potential difference in an uniform B field perpendicular to it's motion is : dE=B.Vp.dx, where Vp is the component of the velocity perpendicular to the wire. Looking to the big wire I tried to take an arbitrary point express dE in function of...

a) since the eletric field is perpendicular to the inicial velocity, the x component is constant, hence Vf.cos45=Vo. This gives Vf=0,6√2.C b) Ei=γi.Eo , γi=5/4 , Ef=γf.Eo , γf=5/(2√7) Finally, Ei+e.E.d=Ef. Apparently this is incorrect, why??

dv/dt is the acceleration, so I thought I could find the acceleration from F = qE = ma = dp/dt. But this is a relativistic case, so the proper acceleration is a = F/mγ3, where v in the gamma is the v of the electron and F = eE. However, I'm not sure if this is correct, because the constant τ...

Does this remain constant and what is direction

Lorentz Law says that for a charged particle moving with a velocity v in a magnetic field B then the force on it is given by $$ \mathbf{F} = q (\mathbf{v} \times \mathbf{B}) $$ Now, if I say that particle’s velocity and the magnetic field are aligned then according to Lorentz Law there will be...

Since I am only required to find the on-axis field, I tried directly integrating the biot savart to find the field, rather than integrating to find the vector potential before taking the curl. However, on integration (by mathematica) it seems that the solution is an elliptic integral, very...

Hello so my doubt is when i are teaching about eletromagnétic filds the frist time a do a representatios is of a full field i Draw the two waves, ume perpendicular to another, and istill i know that's not the best representatios because i should have to rolate the wave while a draw. Later in...

[moderators note: moved from technical forum, so no template] Summary: I can't tell where the mistake in my process is. The computer keeps telling me I am wrong. The Question: What is the electric field at point 1 in the figure? Give your answer in component form.(Figure 1)Assume that a =...

I am reading Michael Field's book: "Essential Real Analysis" ... ... I am currently reading Chapter 9: Differential Calculus in $$\mathbb{R}^m$$ and am specifically focused on Section 9.2.1 Normed Vector Spaces of Linear Maps ... I need some help in fully understanding Theorem 9.2.9 (3) ...

In his book on electrodynamics, Griffith talks about the magnetic field outside a solenoid. Firstly instead of dealing with a typical solenoid with closely wound loops, he instead works with a cylinder with a surface current that has no z-component. To get the angular component of the B-field...

Summary: What is meant by port CARP ASIC functionality to a field programmable Gate Array FPGA. And what is Acronym CARP? What is meant by port CARP ASIC functionality to a field programmable Gate Array FPGA. And what is Acronym CARP?

I am reader Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.1 Linear Algebra ... I need some help in fully understanding the differences between Andrew Browder and Michael...

I'm not so sure how to begin with this problem. I was thinking of usign superposition. I think that the field on the conductor due to the parallel segments of the coil is zero, since Ampere's Law tells us that the field outside the solenoid is zero, right? For the perpendicular segments, I used...

If a charge was placed inside an electric field, where the electric field was equal to zero, what effect would the charge have?

Hi everyone, I am most likely the least scientifically minded person to ever have visited these forums! I'm here with a question that I hope someone more scientifically minded can answer for me. If a pair of plastic coated axial neodymium magnets are installed either side of a sheet of alloy...

Given the example g = \frac{GM}{R^{2}}, we may compute the change in field strength if the mass is changed by a small amount dM to be$$dg = \frac{G dM}{R^{2}}$$and also if R is changed by dR,$$dg = \frac{-2 GM dR}{R^{3}}$$If, however, both the mass and radius are changed by a small amount at the...

I was thinking about this while solving an electrostatics problem. If we have a vector ##\vec V## such that ##\oint \vec V \cdot d\vec A = 0## for any enclosed area, does it imply ##\vec V = \vec 0##?

$$\mathbb{R}^n$$ is a vector space but not a field because it lacks a suitable multiplication operation between pairs of its elements ... Why don't mathematicians define a multiplication operation between a pair of elements and investigate the resulting field ... For example ... why not define...

So I'm reviewing old lectures to prepare for an exam soon. This is about polarization. E fields, D Fields, etc. My professor labeled this diagram like so. The figures my professor drew are cavities in a dielectric if you can't read her handwriting. However, I can't seem to figure out why the...

Hi, My understanding of quantum physics is very basic. I have read that each electron has its own magnetic field; in other words, each electron acts like a mini bar magnet. I was reading about Lenz's law and an unrelated point started confusing me. I was reading this text about Lenz's law...

Thus I assume that one slab has positive charge Q1 and the other slab has negative charge Q2 = -Q1 There are 4 cases for the electric field: 1. x <= -a 2. -a <= x <= 0 3. 0 <= x <= a 4. a <= x The general case: Charge Density ##\rho = \frac {Q} {V}## Flux of E ##\phi_e = \oint \vec E \cdot d...

Hi, been a while since I last asked here something. I am restudying electrostatics right now, and I am facing difficulties in the following question: My attempt: I tried to use Gauss' law, what I got is the equation in the capture but that doesn't lead me anywhere as I am unable to find a...

I begin by calculating the flux to be the flux of the cylinders lateral surface, which equals E*2*pi*p*h (p is the radius) The other two surfaces have E ortogonal to dA, so their flux is 0. Using Gauss law together with the calculated flux above, I get Flux = Q/e Flux = E*2*pi*p*h Solve for E...

I'm not sure how I'm able to calculate the velocity of the particle using the formula without knowing the force exerted on it. Also, I don't understand why the question also provides the mass of the electron.