All Questions
31
questions
0
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2
answers
49
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Validating Basic Laws of Magnetostatics [closed]
I am having trouble with the following problem, although with similar problems I run into the same issue when it comes to validation. The example problem below is a problem for Amperes Law.
The ...
0
votes
1
answer
593
views
Vector potential of a square loop [closed]
I am doing my homework and I'm really stuck on this problem. It asks for the magnetic field due to a square, lying in the $xy$-plane, of side lenght $a$ and with a electric current $I$ running ...
- 154
3
votes
1
answer
2k
views
Magnetic field due to a finite-length straight wire carrying a constant current [closed]
My question: I want to find an expression at any point in space for the magnetic field $\mathbf B$ produced by a straight wire of finite length $L$ carrying a constant current $I$.
I think that we can ...
- 344
1
vote
1
answer
302
views
Magnetic field in two conducting parallel plates. (stripline) [closed]
Studying Poynting Vector power density I found a geometry that I really can't figure it out and is nowhere to be found on the internet.
I have two conducting parallel plates with opposite surface ...
1
vote
1
answer
37
views
A confusing problem in electro- and/or magnetostatics: two parallel cylinders with opposite currents
I got the following problem as a part of my assignment in physics:
Equal but opposite currents $J$ flow on the surfaces of two cylinders of radii $R_1$ and $R_2$, respectively, with the axes of the ...
- 43
2
votes
1
answer
878
views
Why should there be an induced electric field if magnetic field is constant? [closed]
Problem statement:
The curved surface of a very long hollow non conducting cylinder of radius $R$ is uniformly charged with surface charge density $\sigma$. A non conducting small circular ring of ...
- 362
1
vote
2
answers
331
views
How to find magnetic field as a function of $r$ from axis of solenoid?
I was solving this problem:
Whose answer is given as:
I understand the part for calculating the field outside the cylinder, but for inside, I don't get it. If we apply Ampère's circuital law by ...
- 362
0
votes
1
answer
663
views
Magnetic field of coaxial cylindrical capacitor
I have a coaxial cylindrical capacitor as shown, with inner radius a and outer radius b.
The potential difference across both cylinders is V. I need the magnetic field everywhere when the inner ...
- 21
4
votes
1
answer
1k
views
Current density $\mathbf{J}$ of particle with magnetic dipole moment $\mathbf{m}$ [closed]
I'm solving some excercises on magnetostatics, and encounterded this on which i'm having some trouble. Given a particle of magnetic dipole moment $\mathbf{m}$, show that its current density is given ...
- 97
-1
votes
1
answer
878
views
Cylindrical shell in magnetic field [closed]
Exercise: 'Infinitely long cylindrical shell of inner radius a and outer radius b of material of magnetic susceptibility χ is placed in otherwise uniform magnetic $B_0$ perpendicular to cylinder's ...
1
vote
0
answers
207
views
How to calculate the magnetic field of two cylinders when one of them is rotating
Given is the voltage U and the Angular velocity $\omega$. The rotating cylinder is inside the other cylinder and U is measured between them.
To calculate the magnetic field, I tried to solve
$\oint ...
- 23
0
votes
1
answer
3k
views
Obtaining the magnetic vector potential inside an infinite cylinder carrying a z directed current:
Suppose we have a nonmagnetic conducting cylinder of radius $ \alpha $ directed in the z direction, with a current density $ J_{0} \hat{a_{z}} $. What is the magnetic vector potential for $\rho < \...
1
vote
1
answer
3k
views
Deriving Ampere's law from Biot-Savart equation [closed]
As an exercise, I've been trying to derive Ampere's law from the Biot-Savart equation (in the static case). So basically I'm trying to prove:
\begin{equation}
\nabla \times \vec{B}(\vec{r}) = \mu_0\...
- 71
-2
votes
1
answer
176
views
Consider three infinitely long thin wires [closed]
Each carrying current I in the same direction , are in $x$-$y$ plane. The central wire is along the $y$ axis, while the other along $x=+d$ and $-d$
Find the locus of points for which magnetic field ...
- 41
0
votes
0
answers
42
views
Two ways, different result: Find torque due to magnetic force on a conductor
We have an AB conductor of length $2L$ and an infinite one coming out of the screen as shown in the picture (a is the distance between the 2nd conductor and the middle of the finite conductor)
...
- 351
1
vote
2
answers
4k
views
Biot-Savart law and magnetic field of a ring
I have to calculate the magnetic field along the axis of a ring of radius $R$ on which circulates a current $I$ using the Biot-Savart law. The Biot-Savart law as given in my (really bad) course states
...
- 4,736
2
votes
2
answers
569
views
Find torque due to Lorentz force - Wrong result [closed]
Current I is coming from the Z axis and then it flows out uniformly towards the circumference of this disk. The disk has thickness t and Radius R. There is also a constant B field in the Z direction(...
- 351
4
votes
1
answer
3k
views
Finding the vector potential of a spinning spherical shell with uniform surface charge?
I have problem solving the following magneto-static problem. I would greatly appreciate help and guidance.
This is how the problem is stated:
A spherical shell of radius $R$, carrying a uniform ...
- 1,135
13
votes
2
answers
5k
views
Deriving Biot-Savart Law from Maxwell's Equations
As an exercise, I've been trying to derive the Biot-Savart law from the second set of Maxwell's equations for steady-state current
$$\begin{align}&\nabla\cdot\mathbf{B}=0&&\nabla\times\...
- 838
0
votes
1
answer
856
views
Induced current in a circular loop [closed]
In this question I tried using right hand thumb rule for long wire to get magnetic field into plane of paper which induces clockwise current in Loop,again by thumb rule. The problem arises when force ...
6
votes
2
answers
2k
views
Derivation of Ampere's Law in Jackson
The derivation of Ampere's Law in Jackson E&M from the Biot Savart law is for the most part fairly traditional, using the $\nabla\times(\nabla\times A)$ identity on the vector potential:
$$\nabla\...
- 838
3
votes
2
answers
2k
views
How can we apply Ampère's circuital law in a wire?
How can we apply Ampere's circuital law in a wire to calculate magnetic field around a straight current carrying wire? The length of the wire is not infinite.
Using the Biot-Savart law we get
$$B = ...
- 2,091
1
vote
2
answers
2k
views
How to get image current in magnetostatics? (magnetic slab)
I want to know the image current and its location which satisfies the boundary condition at the interface.
This problem was originated from the problem 6-33 in Fields and wave electromagnetics, D. ...
- 209
0
votes
1
answer
1k
views
Magnetic field between two rings [closed]
Two rings are placed parallel atop each other along an axis with a distance $\epsilon$ which is much smaller than the radius of both rings a. Through one of the rings there is a current I and through ...
- 41
0
votes
1
answer
2k
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The magnetic field between two intersecting cylinders [closed]
Consider a cable of infinite length whose section has the form of two intersecting circles of same radius $a$. The first part is then a cylinder of constant volume current density $J$ along the ...
- 183
0
votes
1
answer
2k
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Magnetic Field Along the Axis of the Current Ring - Alternative way to compute
This is Example 5.6 in Griffith's Introduction to Electrodynamics (4th Edition):
Find the magnetic field a distance $z$ above the centre of a circular loop of radius $\ R$, which carries a steady ...
- 3,719
0
votes
1
answer
2k
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Finding the vector potential of an infinite cyclinder with uniform surface current
This is the second part of a problem in Griffith's "Introduction to Electrodynamics 4th Edition" (problem 6.16).
The first part was to find the magnetic field inside a coaxial cable (2 concentric ...
- 342
1
vote
1
answer
1k
views
How do you show that the normal derivative of the magnetic vector potential is discontinous across a surface current?
This is from Griffith's "Introduction to Electrodynamics" 4th edition, problem 5.33.
I need to show that
$$
\tag 1 \frac{\partial \textbf{A}_{above}}{\partial n}-\frac{\partial \textbf{A}_{below}}{\...
- 342
3
votes
2
answers
705
views
Challenging Magnetostatics Problem - the "blind spot" of a magnetic dipole
I'm reviewing for an electromag exam and I stumbled upon a problem that's really hard to figure out. Here it is:
A small magnetic dipole with moment $\vec m = m_o \hat z$ is in a region with uniform ...
- 197
2
votes
1
answer
8k
views
Magnetic field of uniformly charged rotating hollow sphere
I want to compute the magnetic field due to a homogeneously charged, rotating sphere with radius $R$, angular velocity $\vec{\omega} = \omega\hat{z}$ and total charge $Q$. I want to use Biot-Savart ...
- 356
1
vote
1
answer
33k
views
Magnetic field inside and outside cylinder with varying current density [closed]
I am reading through Introduction to Electrodynamics by David J. Griffiths and came across the following problem:
A steady current $I$ flows down a long cylindrical wire of radius $a$. Find the ...
- 1,224