1. Mar 29, 2008

### Nusc

1. The problem statement, all variables and given/known data

Find the charge and current distributions for

V(r,t)=0 A(r,t) = -1/(4*pi*epsilon) q*t/r^2 r-hat

2. Relevant equations

We know
E=1/(a*pi*epsilon) q/r^2 rhat
B = 0
3. The attempt at a solution
What formula do I use?

We know grad x B = mu*J +mu*epsilon dE/dt

Would this suffice to solve for J?

2. Mar 30, 2008

### pam

Apply the wave equation for A.

3. Mar 30, 2008

### Nusc

Typo:

E=1/(4*pi*epsilon) q/r^2 rhat

4. Apr 1, 2008

### Nusc

The answer is pho = q*delta(r)^3 r a vector

How do you get this?

5. Apr 1, 2008

### pam

Sorry, the wave equation won't work here, because this A and phi are not in the Lorentz gauge.
Use $${\vec E}\sim -\partial_t{\vec A}$$.

Last edited: Apr 1, 2008
6. Apr 1, 2008

### Nusc

This is quesiton 10.3 in griffith

7. Apr 1, 2008

### Mindscrape

What is the whole point of using potentials? I'll answer this one for you, it's because two of maxwell's equations are automatically solved with potentials. The no magnetic monopoles equation and Faraday's Law are solved, bam, done.

So, how do E and B relate to the potentials?

8. Apr 2, 2008

### Nusc

I got it, problem solved.

9. Apr 2, 2008

### Nusc

Given B = z hat

B=Curl A

How does one find A?

10. Apr 3, 2008

### Nusc

A is dependent on t so denote A(t)

11. Apr 3, 2008

### Nusc

We know that Div B = 0 but how does that help? I took the divergence of both sides and it gets me nowhere

12. Apr 3, 2008

### Mindscrape

It will depend on what kind of gauge you are using, of which there are infinite. The Lorentz gauge is the most standard since it can handle special relativity, and it has a vector equation of

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

which you should recognize as being similar to the electrostatic potential, with a time term in there, so you can just guess that the solution will be

$$\mathbf{A} = \frac{\mu_0}{4 \pi} \int \frac{\mathbf{J}(\mathbf{r'},t_r)}{\cal{R}} d\tau'$$

where tr is known as a retarded time

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

13. Apr 3, 2008

### Nusc

Given B = Bo*t/tau z-hat where tau and Bo are constants?

14. Apr 3, 2008

### Mindscrape

Will give you the current density.

15. Apr 4, 2008

### Nusc

Using which formula?

16. Apr 5, 2008

### Nusc

ARe you sure this is true, I was told that this is not a requirement.

Now, given B. How do I find A and Which formula do I use?

17. Apr 6, 2008

### pam

You are given A. I showed you how to get E.
B=curl A=0.
You should find that E just equals Coulomb field of a point charge.

18. Apr 6, 2008

### Mindscrape

Basically Maxwell's equations give you everything you ever wanted. It is imperative that you know how to manipulate them.

19. Apr 6, 2008

### Nusc

This is a different question, I had already solved the one in the first post.

Given B = Bo*t/tau z-hat where tau and Bo are constants how does one find A?

B = grad A What rule do I need to apply to solve for A?

20. Apr 6, 2008

### Mindscrape

Practically, it's kind of stupid to convert B into a potential because B is what you are always after, well usually H, but all you have to do is find the current density from B, using maxwell's equations, then go to A.

$$\nabla \times B = \mu_0 (\mathbf{J} + \mathbf{J_D})$$