A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a magnetic field that varies with location will exert a force on a range of non-magnetic materials by affecting the motion of their outer atomic electrons. Magnetic fields surround magnetized materials, and are created by electric currents such as those used in electromagnets, and by electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, they are described as a map assigning a vector to each point of space or, more precisely—because of the way the magnetic field transforms under mirror reflection—as a field of pseudovectors.
In electromagnetics, the term "magnetic field" is used for two distinct but closely related vector fields denoted by the symbols B and H. In the International System of Units, H, magnetic field strength, is measured in the SI base units of ampere per meter (A/m). B, magnetic flux density, is measured in tesla (in SI base units: kilogram per second2 per ampere), which is equivalent to newton per meter per ampere. H and B differ in how they account for magnetization. In a vacuum, the two fields are related through the vacuum permeability,
B
/
μ
0
=
H
{\displaystyle \mathbf {B} /\mu _{0}=\mathbf {H} }
; but in a magnetized material, the terms differ by the material's magnetization at each point.
Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. Magnetic fields and electric fields are interrelated and are both components of the electromagnetic force, one of the four fundamental forces of nature.
Magnetic fields are used throughout modern technology, particularly in electrical engineering and electromechanics. Rotating magnetic fields are used in both electric motors and generators. The interaction of magnetic fields in electric devices such as transformers is conceptualized and investigated as magnetic circuits. Magnetic forces give information about the charge carriers in a material through the Hall effect. The Earth produces its own magnetic field, which shields the Earth's ozone layer from the solar wind and is important in navigation using a compass.
For this problem,
The solution is
However, I would like to understand how to solve this using Biot–Savart Law.
So far my working is:
## \vec {dB} = \frac {\mu_0Ids\sin\theta} {4\pi r^2}##
However, I'm not sure what to do about the ## r^2 ## since the wire is infinitely long. I am thinking...
For part (c) of this problem,
My working is
However, the tricky part is to find theta. I tried to draw the situation so that I could find theta:
It appears that theta = 90 degrees. However, this does not seem to be correct. Does anybody please know how to correctly find theta in terms of...
For this problem,
The solution is,
However, is the reason why they don't include electrical potential energy because the time interval for which we are applying conservation of energy over is very small so the change in electric potential energy is negligible?
Also, when they said, "electrons...
Hello,
I am wondering if it is possible to calculate the B-field of a conductor above an iron plate just using the complex image method. To keep it simple let’s consider a 2D calculation, the metal plate is infinitely deep and wide and the conductor is infinitely long and thin. If the metal...
Summary:: Please see the attached photo.
I have obtained the correct answer, and my solution agrees with the official solution. However, I have some questions about why the solution is correct. (One may have to draw out some diagrams for this problem, it was quite hard to visualise for me.)...
The physics behind this problem is that an electric field is induced (by Faraday's Law), when the B field is switched on. Charges on the ring now experience a force as given by dF = E dq. Apparently, because of this, the ring starts rotating.
I understand that charges in an insulating material...
There’s a current i in the loop in the figure. The Ampere’s force iLB on a wire of length L exerts on charges in the wire but it does no work on the charges. The charges would go in circular motion if there were no wire. Then the wire exerts exactly iLB on those charges to keep the charges...
Problem 52:
A solenoid is 40 cm long, has a diameter of 3.0 cm, and is wound with 500 turns. If the current through the windings is 4.0 A, what is the magnetic field at a point on the axis of the solenoid that is (a) at the center of the solenoid, (b) 10.0 cm from one end of the solenoid, and...
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...
We have a retarded magnetic vector potential ##\mathbf{A}(\mathbf{r},t) = \dfrac{\mu_0}{4\pi} \int \dfrac{\mathbf{J}(\mathbf{r}',t_r)}{|\mathbf{r}-\mathbf{r}'|} \mathrm{d}^3 \mathbf{r}'##
And its curl, ##\mathbf{B}(\mathbf{r}, t) = \frac{\mu_0}{4 \pi} \int \left[\frac{\mathbf{J}(\mathbf{r}'...
Hey everyone
So this is question shown below
I'm not so sure where to begin with this, but I thought I'd work out the net magnetic field first
How would I work out the magnetic field strength that is acting on the vertical current-carrying wire. Since I do not know what d is in this case...
This is the problem, first time i am attempting the Ampere's law problem
From the above question this is my attempt, the picture is
∫B.ds = μ*Ienc; ----> Ampere law , where Ienc is the current enclosed in the amperian loop.
I assume the circle as the amperian loop, is it correct? Can i...
I can't for whatever reason figure out where the sin(theta) term is coming from in the attached picture of page 306 of Griffiths' 4th edition EM text. The paragraph says it comes from the dot product, but I just don't see where it's coming from.
I just tried to find the eigenvalues (for the energy), obtaining E = ±(γħ.√(Bo² + Γo²))/2 and the corresponding eigenvectors for the H matrix. But I don't know what to do to create de state vector χ.
Homework Statement
We have a circular loop of wire, with AB is another wire which is also the diameter of the circular loop. The direction of magnetic field is perpendicular to the loop, into the plane of paper. The magnetic field strength is decreased at a constant rate, without changing the...
If a capacitor is being discharged and the electric field is varying with time producing the displacement currents, wouldn't it be possible to align a time-varying external magnetic field with the magnetic field produced by the displacement currents to increase the discharge rate? Or the...
Homework Statement
Homework Equations
Faraday's Law, Ohm's Law, definition of current[/B]The Attempt at a Solution
We were given this solution:[/B]
The above solution is leaving out a lot of intermediary steps. I don't agree that "the axis of the coil is at 20°, not 70°, from the...
Homework Statement
Not sure if the link is showing. But it's imgur.com/a/LEvd0
Homework Equations
The steps I've taken so far as written in the attempt section below is correct.
The solution provided then proceeds with letting ##z = x + iy## and setting ##\ddot z+i \omega \dot z = 0##. Then...
Homework Statement
Determine the B-field inside the middle of a circular loop of current.
Homework Equations
Attempt at using Ampere's law: ##\oint \vec{B} \cdot d \vec{l} = \mu_0 i##
The Attempt at a Solution
##\oint B \cdot R d \theta = \mu_0 i \Rightarrow BR(2 \pi) = \mu_0 i \Rightarrow B...
Homework Statement
A circular loop of radius a and resistance R is placed in a changing magnetic field so that the field is perpendicular to the plane of the loop. The magnetic field varies with time as B(t) = B_0 * e^(-t) where B_0 is a constant. Determine the electrical power in the circuit...
Homework Statement
Homework EquationsThe Attempt at a Solution
I have difficulty in solving part (C).
The surface bounded by the Amperean loop is like an open drum.
The current enclosed by the loop is ## I_{en}## = I through the bottom of the drum + I(s) through that part of the curved...
Homework Statement
Homework EquationsThe Attempt at a Solution
Because of the external magnetic field ##\vec B_0 ## , a uniform magnetization will be in the direction of external magnetic field.
Because off this uniform magnetization, there will be a uniform magnetic fied in the direction of...
Homework Statement
I came across a pretty interesting question that asks for magnetic flux density (B-field) on the axis of the equilateral triangle. This axis is meant to be perpendicular to triangle's surface passing through its centroid. Assuming that a triangle has sides denoted ##a## and...
, simple, Now I wonder what happens, I have a say speaker magnet or more precisely only the metal end plates that direct the b field lines or any other metal plate designed to guide a b field into a gap of sorts.
Say I now apply a permanent neodymium magnet which has a magnetic field strength of...
Homework Statement
[/B]
A proton is accelerated from rest at the positive plate of two charged parallel plates with a potential difference of 2000 v. After leaving the plates through a small hole in the negative plate, it enters a uniform magnetic field of 0.50 T in a direction perpendicular to...
Hello, I'm a student of electrical engineering. This task appeared in one of the past exams. I've been using the procedure I believe should yield the correct result, however, it turns out I was wrong. Could somebody please check out where the mistake lays in my calculations?
Homework Statement...
Take a spin-1/2 particle of mass ##m## and charge ##e## and place it in a magnetic field in the ##z## direction so that ##\mathbf B=B\mathbf e_z##. The corresponding Hamiltonian is
$$\hat H=\frac{eB}{mc}\hat S_z.$$
This must have units of joules overall, and since the eigenvalues of ##\hat S_z##...
Homework Statement
2b. Suppose the a third wire, carrying another current i0 out of the page, passes through point P. Draw a vector on the diagram to indicate the magnetic force, if any, exerted bon the current in the new wire at P. If the magnitude of the force is zero, indicate that...
Hello!
So I've been working on proving to myself different parts of https://ocw.mit.edu/courses/nuclear-engineering/22-611j-introduction-to-plasma-physics-i-fall-2003/lecture-notes/chap2.pdf packet for several weeks.
Under 2.1 Uniform B field, E=0, for the Larmor Radius, I need to know...
Hi.
If a planar wire loop is moved through a homogeneous magnetic field (field lines perpendicular to the loop plane) with constant velocity and no rotation, Lorentz force will move some electrons to one side of the loop, creating a potential difference. But how does this work with Faraday's...
Homework Statement
Basically having a problem when trying to theoretically calculate the mass of alpha particle in a charged field.
r is the unknown radius of curvature
m = mass of an alpha particle (6.646 *10^-27 kg)
v = velocity of an alpha particle immediatly after decay (1.381 *10^7 m/s)...
Homework Statement
I=10A,L=0.5m,a=0.3m,x=0.2m
Homework Equations
The Attempt at a Solution
by the Biot-Savart Law
ds cross r=-dxcosθ k(direction k)
dB= μI/4π∫-dxcosθ/r^2
B=μI/4π∫-dxcosθ/r^2 (from ?? to ??) in magnitude
question:
1) what is ?? to ??
2)how dx and r respect to dθ?
[/B]
Homework Statement
A 0.300 m radius, 487 turn coil is rotated one-fourth of a revolution in 4.17 ms, originally having its plane perpendicular to a uniform magnetic field. (This is 60 rev/s.) Find the magnetic field strength needed to induce an average emf of 10,000 V.[/B]Homework Equations
E...
Homework Statement
A little stuck on the second question it basically boils down to not quite understanding the question. Was hoping someone here could push me in the right direction. The Question is two part, already completed the first half but wouldn't mind if someone looked over it while...
Hello, first off, I'm not sure if I put this question in the right place so sorry about that.
Given Bi = 1/2 εijk Fjk how would you find F in terms of B? I think you multiply through by another Levi-Civita, but then I don't know what to do after that. Any help would much appreciated.
Can anyone way in on the correct Formulas of a Solenoid Magnetic B-field at Ending, Middle and Outside?
I have the following so far but some of them seem to contradict one another . Photo #1:
Photo #2:
Photo #3:
Photo #4:
Photo #5:
Photo #6:
Homework Statement
Two long rods with distance between them a=100mm, over those two rods there's another rod sliding, friction between them is negligible. The rods are placed in homogenous magnetic field whose B is equal 1T, with direction shown in the picture, between the rods there is voltage...
When we dissect the photon we find an electric field and a magnetic field according to Maxwell. In order to determine the propagation mechanism of a single photon through the fabric of space-time, is there an experimental apparatus designed to determine which field may plow the path, in order...
Homework Statement
Two radioactive isotopes of singly charged plutonium(Pu-249 and Pu-244) are accelerated through a potential difference of 3.00kW and enter a uniform magnetic field of 1.50T directed perpendicular to their velocities. By performing relevat calculations, show that the ratio of...
In string theory, the Neveu-Schwarz B-field appears in the action:
S_{NS}=\frac{1}{4\pi\alpha^\prime}\int d^2\xi\;\epsilon^{\mu\nu}B_{ij}\partial_\mu X^i\partial_\nu X^j.
In Polchinski's text, the antisymmetric tensor appears in the form of
\frac{1}{4\pi\alpha^\prime}\int...
Hi,
I am trying to derive the path length of a charged particle in a B-field. I am assuming the particle will travel a distance L along the applied field. Using the following equations for the path length of a helix and gyroradius:
Helix defined as
[a*cos(t),a*cos(t),b*t] for t on [0,T] has...
An alpha particle is moving in the positive x direction with a speed of 0.0050c = 1.50 * 10^6. When the particle is at the orgin, find the magnetic field at a) P3: x = 1.0,y = 1.0,z = 1.0
The book answer is r3 = sqrt(3) = 1.73 and vecto r3 from q to p3 and vector v form a plane that makes...
Homework Statement
The position of a proton at time t is given by the distance vector
\vec{r}(t) = \hat{i}x(t) + \hat{j}y(t) + \hat{k}z(t)
A magnetic induction field along the z-axis, \vec{B} = \hat{k}B_{z} exerts a force on the proton
\vec{F} = e\vec{v}\times\vec{B}
a.) For...
Homework Statement
Find the current density as a function of distance ##r## from the axis of a radially symmetrical parallel stream of electrons if the magnetic induction inside the stream varies as ##B=br^a##, where ##b## and ##a## are positive constants.
Homework Equations
The...
Homework Statement
Time Varying Current carrying wire creates time varying magnetic field.How can we analytically calculate electric field at distance r from the time varying current carrying wire?
I(t) is time varying current
where α , β are angle of two ends of current carrying wire...
Homework Statement
Homework Equations
The Attempt at a Solution
To be honest I'm clueless. I've missed a large amount of the course and just struggling to find any sources that explain this. I don't want the answer to the question, I want to figure that out for myself. What I really need is...