- #1

- 754

- 2

**em**

**1. Homework Statement**

In a certain region, the magnetic field as a linear function of time is given by

[tex]

B = Bo \frac{t}{/tau} z hat

[/tex]

Bo and tau constants.

A)FInd a simple expression for the vector potential which will yield this field.

B)Assuming the scalar potential is a constant, find E from the above result for the vector potential. Check that your answer is consistent with the diff form of faradays law

**2. Homework Equations**

[tex]

\nabla^2 \mathbf{A} - \mu_0 \epsilon_0 \frac{\partial^2 \mathbf{A}}{\partial t^2} = -\mu_0 \mathbf{J}

[/tex]

[tex]

\mathbf{A} = \frac{\mu_0}{4 \pi} \int \frac{\mathbf{J}(\mathbf{rsingle-quote},t_r)}{\cal{R}} d\tausingle-quote

[/tex]

[tex]

t_r \equiv t - \frac{\cal{R}}{c}

[/tex]

**3. The Attempt at a Solution**

[tex]

B= \nabla \times A

[/tex]

We take the curl of B on the LHS and on the RHS we have

[tex]

\nabla \times (\nabla \times A )

[/tex]

Eventually we will get to this [tex]

\nabla^2 \mathbf{A} - \mu_0 \epsilon_0 \frac{\partial^2 \mathbf{A}}{\partial t^2} = -\mu_0 \mathbf{J}

[/tex]

This is assuming were in the Lorentz Gauge, we don't know if we are. Or do we assume we are? We have to satisfy E = -delV -dA/dt but we don't know either of those quantities.