All Questions
Tagged with electromagnetism derivatives
7
questions
2
votes
2
answers
77
views
$i = \frac{dq}{dt}$ implies $\Delta q = i \Delta t$? Incorrect mathematics used as some kind of hand-wavy justification for an engineering equation?
I am reading an electrical engineering textbook that states that the relationship between current $i$, charge $q$, and time $t$ is
$$i = \dfrac{dq}{dt} \tag{1}$$
Based on this, the authors then state ...
- 4,322
3
votes
0
answers
104
views
Why is electric potential function in free space infinitely differentiable?
Electric potential function in free space of a continuous charge distribution $\rho'$ distributed over volume $V' \subset \mathbb{R}^3$ is denoted by:
$\psi (x,y,z): \mathbb{R}^3 \setminus{V'} \to \...
- 1,141
0
votes
0
answers
103
views
What is meant by rate of change with respect to volume?
In physics we often come across $$\rho=\dfrac{dq}{dV}$$
Does it mean:
$(i)$ $\displaystyle \lim_{\Delta V \to 0} \dfrac{\Delta q}{\Delta V}$
OR
$(ii)$ $\dfrac{\partial}{\partial z} \left( \dfrac{\...
- 1,141
0
votes
0
answers
33
views
Higher dimensional FTC in electrostatics : Does it has mathematical rigor?
I have two volumes $V$ and $V'$ in space such that:
$∄$ point $P$ $\ni$ $[P \in V ∧ P\in V']$
$V$ is filled with electric charge $q$
$\rho = \dfrac{dq}{dV}$ varies continuously in $V$
$V'$ is filled ...
- 556
0
votes
1
answer
323
views
end-to-end resistance of a truncated cone
Basically the question is the resistance of the whole truncated cone which has top and bottom coal-flaps with radius $r_1$ and $r_2$. I have the $r(x)$ given by a function. I know that I have to ...
- 103
0
votes
1
answer
187
views
The two definitions of the divergence of a vector field?
Now, I am aware that the divergence of a vector field, $\vec{F}$, can be defined in two ways. What I don't understand is why do these equal each other formally?
Definition 1: $$\text{div}\vec{F} = \...
- 11
0
votes
1
answer
119
views
Proof Using Faraday's Law and Ampere's Law
For $E = E(x, y,z, t)$ and $B = B(x, y, z, t)$,
$\nabla \times E = -\frac{\delta B}{\delta t}$ and $\nabla \times B = \frac{1}{c^2} \frac{\delta E}{\delta t}$,
how can I show that $\nabla \times (\...
- 978