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  1. B

    Distance traveled winding around sphere

    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...
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    I don't understand the ranges of the angles in spherical coordinates

    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...
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    Eigenvector of complex Eigenvalues

    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.
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    Eigenvector of complex Eigenvalues

    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...
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    Eigenvector of complex Eigenvalues

    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...
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    Flux through a Sphere

    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...
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    Flux through a Sphere

    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...
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    Flux through a Sphere

    I'm trying to figure out what you guys mean by inner product. I haven't heard this term before.
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    Flux through a Sphere

    I see that you are only doing the ##\hat{r}## direction but I don't know why you would ignore the ##\hat{\theta}##.
  10. B

    Flux through a Sphere

    I did ##sin^4(\theta)## but put 3 up there instead. What we have then is the same since the theta component goes to zero in the integral.
  11. B

    Flux through a Sphere

    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...
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    Flux through a Sphere

    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...
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    Multipying Determinants

    Thank you so much! I guess we hadn't covered that yet.
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    Multipying Determinants

    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...
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    Evaluating Scalar Field

    So just 90° then?
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    Evaluating Scalar Field

    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?
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    Evaluating Scalar Field

    I made a mistake. The question should be: ##\mid 2\hat{r} +3\hat{\theta} \mid##
  18. B

    Evaluating Scalar Field

    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...
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    Divergence theorem

    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...
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    Divergence theorem

    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...
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    Flux through a square and rectangle

    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!
  22. B

    Flux through a square and rectangle

    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...
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