# Finding the magnetic vector potential

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1. Jan 7, 2016

### Je m'appelle

I'm supposed to find the magnetic field, the scalar electric potential and magnetic vector potential for the following electromagnetic wave:

$$\vec{E} = E_0 cos (kz - \omega t) \left \{ \hat{x} + \hat{y} \right \}$$

Alright, the magnetic field goes as

$$\vec{B} = \frac{1}{c} \hat{k} \times \vec{E}$$

$$\vec{B} = \frac{E_0}{c} cos (kz - \omega t) \left \{ \hat{z} \times \hat{x} + \hat{z} \times \hat{y} \right \}$$

$$\vec{B} = \frac{E_0}{c} cos (kz - \omega t) \left \{ \hat{y} - \hat{x} \right \}$$

I used $\hat{k} = \hat{z}$ since the wave seems to be traveling through the z-axis.

Now when it comes to the potentials, I'm lost. I know, for once, that I can't directly apply $V = - \int \vec{E} . \vec{d \ell}$ since the electric field is no longer constant.

Any hints?

2. Jan 8, 2016

### blue_leaf77

You need the additional information about the presence of free charge and current density to solve for the potentials.

3. Jan 8, 2016

### vela

Staff Emeritus
These are vacuum solutions of the wave equation, so you can assume $\rho=0$ and $\vec{J}=0$.

A good place to start (and the reason the template you deleted is supposed to be there) is to find the relevant equations which relate the fields to the potentials.

4. Jan 9, 2016

### Brian T

For the line integral $V = - \int \vec{E} . \vec{d \ell}$, you do not need a constant function to do the integral (maybe review some vector calculus?). You also need to consider what gauge you're using since you have time varying fields.