User:Mgummess/sandbox

$$\mathbf B = \frac{\mu_0 \mathit I}{2 \pi \mathit s} \hat{\boldsymbol{\phi}}$$

$$\hat{\boldsymbol{\phi}}$$

$$\mathbf I = \lambda \mathbf v $$

$$\mathbf J = \rho \mathbf v$$


 * $$\nabla \times \mathbf B = \mu_0 \mathbf J + \mu_0 \epsilon_0 \frac{\partial \mathbf E}{\partial t}$$

$$\mu_0 \epsilon_0 \frac{\partial \mathbf E}{\partial t} = \mu_0 \mathbf J_d$$

$$\frac{\partial}{\partial t} \mathbf E(t)$$

$$-\frac{\partial}{\partial t} \mathbf E(-t)$$

$$\Box^2 \mathit V = -\frac{1}{\epsilon_0} \rho$$

$$\Box^2 \mathbf A = -\mu_0 \mathbf J$$

$$\mathbf B(\mathbf r) = \frac{\mu_0}{4 \pi}\int \frac{\mathbf J(\mathbf r') \times \frac{\mathbf r - \mathbf r'}{|\mathbf r - \mathbf r'|}}{|\mathbf r - \mathbf r'|^2}\ d\tau'$$