All Questions
11 questions
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Deriving the Curl of the Magnetic Field, Role of the Nabla Operator
We know that the magnetic field can be written in the following way:
$$\nabla_{\vec r }\times\vec B(\vec r) = \frac 1 c \nabla_{\vec r}\times\int d^3\vec r_q\ \vec j(\vec r_q)\times \frac {\vec r-\vec ...
- 193
3
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3
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116
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Finding the vector potential
$$\nabla\times\mathbf{B}=\nabla\times\left(\nabla\times\mathbf{A}\right)=\nabla\left(\nabla\cdot\mathbf{A}\right)-\nabla^2\mathbf{A}=\mu_0\mathbf{J}\tag{5.62}$$
Whenever I try to work this out and ...
- 220
0
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1
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183
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Why the divernce of this magnetic field is not zero?
I am working on a project on which I need to calculate the geomagnetic field in different coordinates. When I use the conventional form of the dipole field in spherical coordinates:
$$\vec{B}_{r,\phi}=...
2
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1
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280
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Factor before Dirac delta in magnetic dipole field formula
I bumped into this formula for the magnetic induction field generated by a dipole, containing Dirac's delta, while studying hyperfine splitting: $$\textbf{B}(\textbf{r}) = \frac{2}{3}\mu_0 \textbf{m}\...
1
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1
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604
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Visual representation of the curl of the magnetic vector potential!
I know that the electric field (a vector field) is the result of the gradient of the electric potential,which is a scalar field of the type: $\Phi$ : $\mathbb{R}^3 \rightarrow \mathbb{R}$. So the ...
- 1,628
3
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1
answer
1k
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Erratum in Griffith's Introduction to Electrodynamics
Applying the divergence to Eq. $47$, we obtain
$$ \mathbf{\nabla} \cdot \mathbf{B} = \frac{\mu_{0}}{4\pi} \int \nabla \cdot \left( \mathbf{J} \times \ \frac{\hat{\mathbf{r}}}{r^2}\right) d\tau^{'}. \...
user240696
1
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1
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868
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Derivation of curl of magnetic field [closed]
I am having trouble in one part of derivation of curl of magnetic field, from Biot-Savart law. The attached picture is from Griffiths - Introduction to Electrodynamics.
I got all the parts, but only ...
- 337
1
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3
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143
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Passing from curl to vector product
I don't understand how to obtain second equation with first part in the equation
$$
\nabla \times \vec A_0 e^{-j \vec k\cdot \vec r} = -j\vec k\times \vec A_0 e^{-j \vec k\cdot \vec r}.
$$
Can you ...
- 13
0
votes
1
answer
259
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Confusion in adding constant to magnetic vector potential
The $x$-component of $B$ is:
$B_x=\dfrac{\partial {A_z}}{\partial y}-\dfrac{\partial {A_y}}{\partial z}
=\dfrac{\partial {(A_z+C_1)}}{\partial y}-\dfrac{\partial {(A_y+C_2)}}{\partial z}$
where $...
- 137
0
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2
answers
1k
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Divergence of vector potential [closed]
I was given the vector potential $$\vec A (\vec r) = - \vec a \times \nabla \frac{1}{r}$$ with a constant vector $\vec a$. Now, I found the $\vec B$ field which is I think $- \vec a \frac{2}{r^3}$, ...
- 4,830
7
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6
answers
15k
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Why is curl of current density $\nabla \times \vec{J}$ equal zero?
I am revisiting the derivation for $\nabla \cdot \vec{B} = 0$ in magnetostatics for the field $\vec{B}(\vec{r})$ of a charge $q$ at position $\vec{0}$ with velocity $\vec{v}$. It proceeds like
\begin{...
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