Scalar and vector potentials and magnetic monopoles

1. Apr 16, 2010

peterjaybee

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

Write down expressions oer E and B fields in terms of $$\varphi$$ and $$\bar{A}$$. Demonstrate that this definition of B is consistent with the non-existence of magnetic monopoles.

2. Relevant equations

3. The attempt at a solution

The first part of the question is easy. i.e. bookwork
$$B = \nabla \times \bar{A}$$
$$E = \nabla\varphi - \frac{\partial{A}}{\partial t}\$$

I dont know how to approach the second part of the question though

Last edited: Apr 16, 2010
2. Apr 16, 2010

tiny-tim

Hi peterjaybee!

Hint: there is electric charge, but (if there are no magnetic monopoles) there's no magnetic charge (ie, you can't have a particle or an object with overall magnetic charge) … so how does electric charge come out of the equations in a way that magnetic charge can't?

3. Apr 16, 2010

Cyosis

I believe you're missing a minus sign for the E-field. Grab your book and go to the page where the Maxwell equations are listed. Can you identify the equation that has electric charge as a source term?

4. Apr 16, 2010

peterjaybee

thanks, yes you are right the minus sign should be there.

With regards to the second part, i think I have it thanks to your hints. Div B = 0 is the maxwell eqn that shows there are no magnetic monopoles (as there are no source terms - unlike for div E). The definition of the vector potential is consistent with this because the divergence of a curl is always zero.

5. Apr 16, 2010

Cyosis

Yes that is correct.