Recent content by sittingOnTheFloor

I guess I misunderstood what you meant by expressing x and y in terms of cylinder coordinates then. Could you explain more what you meant by that? And also how do the trig functions make it not completely general?

Ah right well here's where the context of the problems comes in cause this is actually for a program I have to write so as long as it is right it doesn't matter, and it is necessitated that I do keep it in terms of x, y, and z. But if that is right then I would like to thank you a whole whole...

okay, that makes more sense. I can just replace ##\theta## with ##\arctan{\frac {y} {x}}## right, leaving me with \begin{equation} B(x,y,z) = (- \frac {B_1} {2} {\sqrt{x^2 + y ^ 2}}) ({\cos({{\arctan{\frac {y}{x}}}}) \hat x + \sin({{\arctan{\frac {y}{x}}}}) \hat y + 0\hat z}) + ({B_0 +...

By second term do you mean the arctan? That is what I am most unsure about, because you had said that I do need to take theta into account but from the original equation it is 0, so instead of the arctan should it be 0?

Well I am pretty sure the matrix multiplication for this looks like \begin{bmatrix} \cos{\theta} \hat x + \sin{\theta} \hat y + 0\hat z \\ -\sin{\theta} \hat x+ \cos{\theta} \hat y + 0 \hat z \\ 0 \hat x + 0 \hat y + 1 \hat z \end{bmatrix} so does that mean that each row of that matrix is what...

I am considering ##r## to be equal to ##\sqrt{x^2 + y^2}## and ##\hat r## to be ##\cos{\theta}\sin{\theta}\hat x## which doesn't sit well with me but that is my (knowingly wrong) reading of the attached pictures

shoot didn't properly copy what I had written out \begin{equation} B(x,y,z) = - \frac {B_1} {2} {\sqrt{x^2 + y ^ 2}} {\cos{\theta}} {\sin{\theta}}\hat{x} - {\sin{\theta}} {\cos{\theta}} \hat{y} + (B_0 + B_1z)\hat{z} \end{equation} You said the r term was wrong though too did you just mean...

okay this is maybe stemming from my misunderstanding of the ##\theta## term. Are you saying it would be \begin{equation} B(x,y,z) = - \frac {B_1} {2} {\sqrt{(x^2 + y ^ 2}} \hat{x} - {\sin{\theta}} {\cos{\theta}} \hat{y} + (B_0 + B_1z)\hat{z} \end{equation} because this doesn't feel right to...

Homework Statement I have been given a changing magnetic field in cylindrical coordinates. The equation is: \begin{equation} B(r,\phi,z) = - \frac {B_1} {2} r \hat{r} + (B_0 + B_1z)\hat{z} \end{equation} I need to be able to find the magnetic field as a function of x, y, and z. Homework...