Change independent variable in magnetic field line equations

Jarvis323
Messages
1,247
Reaction score
988
How can I convert this system of equations :

$$\frac{dz}{d\phi} = \frac{rB_z}{B_{\phi}},
\frac{dr}{d\phi} = \frac{rB_r}{B_{\phi}},
\frac{d\phi}{d\phi} = 1$$

to

$$\frac{dr}{dz},
\frac{d\phi}{dz},
\frac{dz}{dz}$$
 
Physics news on Phys.org
You can use the chain rule.
Note: the third one is trivial.
 
Thread 'Direction Fields and Isoclines'
I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
Back
Top