Electric Potential Equations: Understanding and Applying in Non-Uniform Fields

[cookiemnstr510510]

Homework Statement

Hello, I am wondering if I am thinking about electric potential correctly:
Stop me if I am wrong:
V=electric potential, the electric potential is created by source charges altering space around them.
If you place a test charge, q, within that space we can say it experiences electric potential energy U.

My book gives me an equation V=U_{q + sources}/q.
since energy is conserved could we say ΔU=-ΔK? furthermore could we say ΔU=-W?
If so I see many possibilities of equations for V.

For a constant electric Field I know that U=qEd, therefore V=qEd/q=Ed
I believe this is just for a constant electric field...
How would the equations change for a non-constant electric field?
I have all these equations and have an okay understanding of them but when I do problems things are just not clicking...any advice/input would be appreciated

 

[kuruman]

If you place a test charge, q, within that space we can say it experiences electric potential energy U.

Add "where U = qV" to this.

The rest of your understanding is fine. Yes, V = Ed is only the case for a uniform electric field. Constant means it does not change with time. Uniform means its magnitude and direction do not change from one point of space to another. You can have a uniform field that is not constant and a constant field that is not uniform.

...any advice/input would be appreciated

Advice on specific problems will be supplied by us when it is needed. Just ask.