Finding an electric field from a scalar field

1. Nov 13, 2005

Noone1982

Say I know an electric field

E = (yz - 2x)x-hat + (xz)y-hat + (xy)z-hat

How do I find the scalar field that would produce that? If I integrate each part I get

Vx = xyz - x^2
Vy = xyz
Vz = xyz

Vt = 3xy - x^2

To find E, I would take E = gradient cross the scalar field, but that would clearly not work. What I am doing wrong?

2. Nov 13, 2005

Physics Monkey

Pick any component you want and integrate. For instance, if you picked the x-component then your guess "answer" would look like $$V = xyz - x^2 + f(y,z),$$ where f is an arbitrary function of y and z. This is because you only know that the partial derivative of V with respect to x is equal to yz - 2x. To figure out what your function f is, make use of your information about the other two partial derivatives of V. Of course, V is still undefined up to a constant.

3. Nov 13, 2005

lightgrav

Each component of the E-Field is the (-) derivitive of the scalar potential with THAT coordinate , yes E is the (-) gradient .

Notice that d(x^2)/dy = 0 , so that E_y cannot give info about purely "x" terms in V, (or x and z terms, either). Similarly, E_x gives no info about purely y or z terms.

Don't add the xyz terms, just make sure they all agree.

Last edited: Nov 13, 2005
4. Nov 13, 2005

Noone1982

Im still fuzzy on how to obtain the unknown function. Can you further explain?

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