What about rho?

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?

What about rho?

2. Mar 30, 2008

pam

Your E is wrong.
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.

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

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