All Questions
31
questions
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
$$\begin{align}&\nabla\cdot\mathbf{B}=0&&\nabla\times\...
- 838
6
votes
2
answers
2k
views
Derivation of Ampere's Law in Jackson
The derivation of Ampere's Law in Jackson E&M from the Biot Savart law is for the most part fairly traditional, using the $\nabla\times(\nabla\times A)$ identity on the vector potential:
$$\nabla\...
- 838
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
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
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
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
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
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
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
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
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
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
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
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
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