Sorry, I don't quite get you. I have searched around about that differential form, I am not sure what should i find with it.
Q = \int\int D \cdot ds = \int\int\int \rho_v dv
The Q is given in the question as a constant, D can be derived out by Coulomb's law.
The answer for the question is
V =...
Homework Statement
- A point charge is placed at the origin of the medium.
- The relative permittivity of the medium, \varepsilon_r = a / r, a is a constant, r is the radius from origin to any point around the charge.
- Objective of this question is to find the expression for voltage.at any...
Sorry, I just notice there are some naming convention problem in my equations, A is a scalar, bacause \nabla can't multiply with a scalar
(\nabla A \cdot\nabla)\vec B
Now I know that the del is not commutative, but I want to conform if this is the right way to evaluate that expression, i have...
so for the right side, it is something like this:
\begin{align}(\nabla\vec A\cdot\nabla)\vec B &= (\frac{dA_x}{dx}\frac{d}{dx}+\frac{dA_y}{dy}\frac{d}{dy}+\frac{dA_z}{dz}\frac{d}{dz})\vec B\\
&= <(\frac{dA_x}{dx}\frac{d}{dx}+\frac{dA_y}{dy}\frac{d}{dy}+\frac{dA_z}{dz}\frac{d}{dz})...
Homework Statement
Is there any difference between these 2 terms, if yes how are they different?
\begin{align}(\nabla\cdot\nabla\vec A)\vec B &= (\nabla\vec A\cdot\nabla)\vec B\end{align}
Homework Equations
From what i know about dot product, it is commutative, so does this property apply here?
Homework Statement
\oint_C{(x^2 + 2y + sin x^2)dx + (x + y + cos y^2)dy}
the contour C formed by 3 curves:
C(x,y) = \begin{cases}x=0, \quad from (0,0) to (0,5)\\y = 5 - x^2,\quad from(0,5) to (2,1) \\ 4y = x^2, \quad from(2,1) to (0,0)\end{cases}
and the Stoke Theorem:
\oint_C \vec F \...
Imagine that the curve revolve around the z-axis, and you can divide this volume into as many cylinders as u like to approximate this volume,
volume of cylinder,
V_{cylinder} = \pi r^2l
but in this case, the r = y, l = dz
thus, your small cylinder volume, dV
dV = \pi y^2 dz
by integrating...
r is the distance of the point-like mass to the center of axis and the L_{rod} is the length of the rode. The point like mass can be moved closer to the center, so the r can be change, but the L_{rod} always fixed at a length.
yeah the Torque and the period symbol almost look the same too...
In my lab manual, the period calculation is:
T^2 = \frac{8m\pi^2r^2}{D} + T^2_0
where the T_0 is the period of oscillation when the mass is removed from the rod.
And the D is stated in my manual that it is the restoring torque...