We know that the magnetic field can be written in the following way:
$$\nabla_{\vec r}\times \vec B(\vec r) =\frac 1 c \nabla_{\vec r} \times\int d^3\vec r_q\ \vec j(\vec r_q) \times \frac {\vec r-\vec r_q}{|\vec r-\vec r_q|^3}$$
and, using the ##BAC-CAB## identity, the curl of this...
I have read Griffiths' Chapter 2 sections on Conductors. According to it, (if I understood it correctly) if the charge is put inside the cavity of a conductor, then the equal and opposite total charge will be induced surrounding the cavity. This charge and the total charge induced surrounding...
I am trying to build a simulator for designing a mass driver. What I am essentially doing is given an iron rod and a coil of wire, calculate the force on the iron rod at various positions along the coil axis. Ideally, I want to use the various forces to calculate the final velocity of the rod...
We have a parallel plate capacitor with two different dielectrics
It seems to be the case that the potential difference on each half of the capacitor is the same.
Initially, the electric field was ##\vec{E_0}=\frac{2\sigma_+}{\epsilon_0}\hat{j}##.
If we were to insert a single dielectric...
I can derive it for a circular loop:
$$dF=BI\sin\phi\ dl=BIr\sin\phi\ d\phi$$
Torque on quarter circle when field is parallel to plane of loop=$$\tau=\int^{(\pi/2)}_0 BI \ dl \sin\phi (r\sin\phi)$$$$=\int^{(\pi/2)}_0 BIr^2 \sin^2\phi\ d\phi$$
Net torque=##4\tau=BIA##
If magnetic field is at any...
Original Question: If a small magnetic compass needle was placed at point Z, what direction would its north pole point? Explain your answer
My try:
Since the current flowed in an anticlockwise loop in the first wire => North pole was formed inside the loop => Outside the wire near the point...
I am trying to work through the MIT free coursework to study Physics before next semester and I am having a heck of a time with the strict answer syntax, or I am having a fundamental issue with the physics, of course.
The problem is from "Week 1: Electrostatics Problem Solving Practice 1 W1PS4...
my sir gave us the above question as homeork,our task to derive why it happens so I couldnt get it right. So today he gave the answer to it. we were also a..sked to find the induced charges on the dielectric surface.
.
E ext : electric field between capacitor plates when no dielectric was put
E...
My attempt:
The electric field in the interior of a conductor is ##0##.
By symmetry, the electric field is directed radially outward.
Take the Gaussian surface as the thin cylindrical shell of radius ##\rm 3\ cm## and length ##L##.
##\displaystyle\oint\limits\vec{E}\cdot d\vec{A} =...
Hello, the Homework Statement is quite long, since it includes a lot of equations so I will rather post the as images as to prevent mistypes.
We need to find the integral
where
with
$$
J_m =(\sqrt{2}(r−ia\cosθ))^{−1} i(r^2+a^2)\sin(θ)j,
$$
$$
J_n = - \frac{a \Delta}{ 2 \Sigma} \sin(\theta...
I'm trying to make sure I understand the g-factor of the electron, so if my question is flawed please don't just point out my flaws, but help me correct my understanding
If I understand correctly the magnetic moment of an object depends on it charge, its mass and its momentum
$$
\mu =...
I'm currently searhing for a magnetohydrodynamics simulator to study how different molten metals interact with variating magnetic fields, is there any free (preferebly) simulator that someone recomends in particular?
And also, is there any way to use Autodesk's CFD to create a MHD simulation?
In the book Electricity and Magnetism by Purcell and Morin, there is the following snippet
My question is how to arrive at ##\vec{F}\cdot\vec{v}## as the rate that work is done?
For a personal project, I need to calculate the EMF induced by a solenoid, the problem is, that the secondary circuit where the eddy currents are formed are outside the solenoid's length but still on it's axis.
The problem comes when i need to calculate the vector magnetic field inductance at a...
In Sadiku, he used the formula dλ=dΨ * Ienclosed/I
to determine the total flux linkage for coaxial cable for ρ<a and for a<ρ<b, but I applied this formula for the solenoid and it didn't work, the way that works for the solenoid is by using λ=N*Ψ.
So why we multiply by Ienclosed/I in the coaxial...
Here is a depiction of the problem
a) The potential at any point P due to a charge q is given by ##\frac{kq}{r}=\frac{kq}{\lvert \vec{r}_s-\vec{r}_P \rvert}##, where ##r## is the distance from the charge to point P, which is the length of the vector difference between ##\vec{r}_s##, the...
Hello all, I am currently studying for a physics a-level qualification in the UK, I use the AQA specification and I am having trouble understanding this image representing a scenario I found in my textbook. The first image in the three part diagram shows this rotating coil and to me, it makes...
I am trying to understand the differences in design between a traditional solenoid with a ferrous plunger vs linear motors that use either induction or permanent magnets. From my understanding, a traditional solenoid, whether DC or AC, cannot fire in both directions with polarity switching since...
Hello All:
read a paper related to electromagnetic force and its applications in acceleration of charges particles , some thing came up in it , they drive a force applied on the particle called Faraday force = [1/2B]* [dB/dt]*m*v
B magnetic field , m mass of the particle , v the velocity of...
It is believed that Maxwell equations (together with other relations depending on the materials) are sufficient to account for any electromagnetic macroscopic effect.
The problem is that, for a Maxwell equation to hold, it must at least be defined.
Consider for example the case of two...
I am currently a sophomore in HS, and I have a science fair project next year. I want to do something interesting- I don't want to put in barely any effort and do something that everyone has done, like 'growing plants in different light levels'.
I would ideally like to do something with...
The electric field inside a charged spherical shell moving inertially is, per Gauss's law, zero.
If the spherical shell is accelerated, the field inside is not zero anymore, but it gains a non-null component along the direction of the acceleration, as mentioned, for example, in this paper.
The...
Hi.
I have solved the problem below as shown in the attached image. However I'm at a loss to figure out where I am making a mistake, and I know it is indeed a big goof up. Requesting guidance over identification and rectification of this big goof up.
(Edit- I can solve this problem in the...
This was a trivial question I had (which I posted here on the PF EM Forum: https://www.physicsforums.com/threads/bound-charges-polarisation-of-a-half-cone.1015308/).
As I received no response on the above link I decided to post the same as a self formulated HW problem. Below I have attached an...
Summary:: There seems to be a mismatch, in the "Maxwell's" equations, between the number of equations and number of variables.
I was trying to play around with the equations for Electromagnetism and noticed something unusual. When expanded, there are 8 equations, 6 unknown variables, and 4...
In Purcell's E&M Section5.3 "Measurement of charge in motion", he said when a charge is in motion, the force on test charges may not be in the direction of radius vector r. And in next paragraph, he defined Q by averaging over all directions.
However, he just measured the radial component of...
In a problem of an oscillating electric dipole, under appropriate conditions, one can find, for the potential vector calculated at the point ##\vec{r}##, the expression ##\vec{A}=\hat{k}\frac{\mu_0I_0d}{4\pi}\frac{cos(\omega(t-r/c))}{r}## where: ##\hat{k}## is the direction of the ##z-axis##...
While reading about electromagnetism from the OpenStax books with my son (and doing some experiments), he asked this question.
Suppose I hang a pendulum and make it oscillate inside a coil connected to a Galvanometer as shown in the schematic diagram:
Hopefully the image is clear enough. His...
I'm preparing for exam but it seems I can't find problems similar to this on the internet.
Here I will apply Gauss's law on the electric field vector to get the charge density. but the problem is that I can't find similar examples on the internet that uses direct vectors on Maxwell's equations...
The electromagnetic field can carry waves, some of them are light, others are used in radio broadcast. These oscillatory waves are distinguished by their frequency. The usual pickup that we get from electric currents in the circuits in the walls of the building has a frequency of about 100...
I want to show that the action staying the same action after taking ##A^\mu \to A^\mu + \partial ^\mu \chi##, for the first term I suceeded in showing the invariance using the fact ##[\partial ^ \mu , \partial ^\nu]=0## but for the second term I'm getting: ##\epsilon^{\alpha\mu\nu}A_\alpha...
Hi, everyone. I just finished studying the principle on which a transformer works. It relies on Faraday's law of induction. And my high school physics book uses the following picture for illustration:
Roughly speaking, the...
I am reading Griffith's textbook on EM. There is a problem asking to find the force acting on the northern hemisphere by the southern hemisphere of a uniformly charged sphere.
The solution idea is to find the expression of the E field by Gauss's law and integrate the force over the northern...
So my idea was that to reach the equilibrium position, the final moment of force has to be 0 (so in the end the forces will “eliminate” each other). And I found the equation Fm=B*I*l*sinα, which should characterize the force, which affects wire with the current in a magnetic field, and Fleming’s...
The experiment consists of a large field coil (connected to a current source) surrounding a coplanar and coaxial small detector coil in the center of the field coil connected to the oscilloscope.
1. Matching Current v. Time Graphs to Oscilloscope Graphs
Example of one pair of graphs (I'll...
Summary:: Can anyone introduce an informative resource with solved examples for learning variation principle?
For example I cannot do the variation for the electromagnetic lagrangian when ##A_\mu J^\mu## added to the free lagrangian and also some other terms which are possible:
$$
L =...
Mary Boas attempts to explain this by pointing out that the situation cannot arise because charges will have to be placed individually, and in an order, and that order would represent the order we sum in. That at any point the unplaced infinite charges would form an infinite divergent series...
At first I take the uniformly distributed charge and then divide it by the area of the carpet to get the surface charge density σ
-10E-6 C / 8m^2 = σ = -1.25E-6C/m^2
Then I divide the surface charge density by 2e0 to get the electric field strength caused by the infinite plane...
The near-range magnetic field ##\vec{B}## of a point charge ##q## at distance ##\vec{r}##, moving at a non-relativistic velocity ##\vec{v}##, is given by
$$\vec{B}=\frac{q}{4\pi\epsilon_0c^2}\frac{\vec{v}\times\hat{r}}{r^2}.$$
Faraday's law of induction for the induced EMF ##V_c## in a coil...
Summary:: Suggest a geometry
Hello! I have difficulties with this question. It is translated from Swedish so if something's weird tell me.
The speakers in headphones often work with the help of magnetism, when a varying voltage is applied across a coil attached to the speaker membrane. The...
If so, what will I measure in the Ampermeter, the zero total current or the value of the conduction current?
I was thinking of the following example- a circuit consist of a current source, an Ampermeter, a switch, and a semiconductor. The semiconductor can have both conduction and displacement...
Purcell says that taking the surface integral of the magnetic field ##\textbf{B}## over the surfaces ##S_{1}, S_{2}, S_{3},...## below is a good way of finding the average of the volume integral of ##\textbf{B}## in the neighborhood of these surfaces.
More specifically, he says in page...
Can anyone please tell me why the torque on a circular current loop can be calculated by the equation below? In other words, what is the intuition for the formula? Thank you. (I modified my question to a particular case)
$$ \vec{\tau} = I \vec{A} \times \vec{B} $$
In my latest 10th grade physics lesson, we were learning about the refraction of light. I decided to share what I knew about why light slows down in a vacuum, which is, in short, because the electric field of the electromagnetic wave exerts a force on the charged electrons of a medium, which in...
Let r = position of the electron = 6mm - 36.8μm; λ = mean free path traversed.
Integrate E(r) = Q/(2πϵLr) between the two shells gives:
V = [Q/(2πϵL)]*log(r/(r-λ))
I know that the question is asking for the voltage at which the electron energy will get to 23eV, but i am unsure how to get rid...
I am required to find the direction of the electric field on the surface of a grounded conducting sphere in the proximity of a point charge ##+q##. The distance between the center of the sphere and the point charge is ##d## and using the method of images we find that the charge of the sphere is...