Yeah, sorry I copied that from the wrong part of my notes. It gets a little cluttered after a while of trying different things.
##\phi(t)=w\frac {R-Rcos(\theta)}{v_z}##
1)##\frac{\partial \phi}{\partial \theta}=\frac{wR}{v_z}sin(\theta) d\theta##
2)##(\frac{\partial \phi}{\partial...
I had this same mental block a while ago. I'd used the limits dozens of times and one day I just couldn't figure out why.
They way I figured it out was as follows:
Picture yourself in a sphere sitting in a swivel chair holding a paint brush so that you're touching the inside of the sphere...
I figure it out:
##(-585+117i)x_1+234x_2=0## where ##x_1=1+i##
##\frac{(-585+117i)(1+i)}{-234}=x_2##
##x_2=3+2i##
This is really exactly the same so I'm not sure what happened up there. Probably just calculations. I used my calculator once I had it in the second equation form.
For whatever reason all of the problems for this section are like this. I just hope our test tomorrow is simpler...
Got ahead of myself on posting. 1 sec while I do what you said.
They did cancel so I'm left with
##(-585+117i)x_1=-234x_2##
##x_1=1+i=\frac{-234x_2}{-585+117i}##
which is...
Homework Statement
##A=\begin{bmatrix} 16 &{-6}\\39 &{-14} \end{bmatrix}##
Homework Equations
The Attempt at a Solution
I did ##A=\begin{bmatrix} 16-\lambda &{-6}\\39 &{-14-\lambda} \end{bmatrix}##
and got that ##\lambda_1=1+3i## and ##\lambda_2=1-3i##
The solution...
I get it, sort of. I understand the math but when I think of flux I think of everything, no matter direction, going through a surface. I want to count all of it, not just what is perpendicular to the surface.
I've finished the problem and it matches perfectly with the divergence of E and...
I know dot product. I've just never heard it called inner product. However, I don't understand, physically, why we would ignore one direction of the field. It's one thing to say if the direction of the field is only in ##\hat{r}## then that is all fine and understandable (if I did the integral...
Okay,
##\int_0^{2\pi}\int_0^{\pi}r^2sin^2(\theta)(sin(\theta)\hat{r}+cos( \theta)\hat{\theta})r^2sin(\theta)d\theta d\phi##
=##2\pi r^4\int_0^{\pi}sin^4(\theta)\hat{r}+sin^2(\theta)cos(\theta)\hat{\theta}##
second integral is zero. first integral evaluates to ##\frac{3\pi}{8}##
so finally...
I was told it might be better to post this here.
Homework Statement
The trick to this problem is the E field is in cylindrical coordinates.
##E(\vec{r})=Cs^2\hat{s}##
Homework Equations
##\int E \cdot dA##
The Attempt at a Solution
I tried converting the E field into spherical...
Homework Statement
This is a practice problem where the solutions are given.
Both are 3x3 matrices.
det A=-2 and det B=1
find the following:
1)det(A6)
2) det(B-1A3B3AT)
3) det(4(AT)2(B-1)4)
4) det((2BT)-1)
Homework Equations
The Attempt at a Solution
I get the first two...
I'm not sure how I would go about finding the angle between the two vectors in spherical. I could probably switch them to Cartesian but is there a simpler way via spherical?
Homework Statement
Evaluate the scalar field ##f(r, \theta, \phi)= \mid 2\hat{r}+3\hat{\phi} \mid## in spherical coords.
Homework Equations
Law of Cosines?
##\mid \vec{A} + \vec{B} \mid = \sqrt{A^2+B^2+2ABCos(\theta)}##
The Attempt at a Solution
I'm not sure the law of cosines...
As soon as I posted this I realized my problem. So, imagining myself in the center of a sphere and my arm pointed out holding a paint brush as the r vector:
I spin 360 degrees painting a line all the way around. Then raising my arm and spinning again I paint a little more above the previous...
Homework Statement
Find the divergence of \vec v = \frac{\hat{v}}{r}
Then use the divergence theorem to look for a delta function at the origin.
Homework Equations
\int ∇\cdot \vec v d\tau = \oint \vec v \cdot da
The Attempt at a Solution
I got the divergence easy enough...
A) its funny that I have done it correctly on paper but incorrectly here. I'm not paying enough attention I guess.
B) no idea why I added those. I'm glad that I at least had the correct idea.
thanks for the help!
Homework Statement
Flux:
a. Calculate the flux of the vector v1 = (1, 3 5) through a 2×2 square in the x-z plane (i.e., y = 0).
b. Calculate the flux of the vector v2=(z, y, -x) through this rectangle:0≤ x ≤3, 0≤ y ≤ 2, z = 0..
The Attempt at a Solution
I guess flux is suppose to be...