# Voltage difference, line integral

1. Feb 21, 2013

### kougou

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

I don't understand the follow formula of the integral :

Integral of ( E dot dL) from B to A

What direction is the dr vector? Is it the direction of the line integral?

Say I want to derive the formula for electric potential due to a point in Space. E has a direction vector of ar
assume dL is pointing from infinity to A (-ar), which is opposite of the Eletric Field. And the formula ends up with a negative sign, which is not consistent with the formal formula.
Why?

Last edited: Feb 21, 2013
2. Feb 21, 2013

### Simon Bridge

The integral is you described, "Integral of ( E dot dL) from B to A", is $$\int_B^A \vec{E}\cdot\vec{dL}$$... that what you meant?

dr points wherever you define it to point.

The integral is along a line, which, in general, will curve in most coordinate systems.
But does the potential difference in an electric field depend on the path taken? What does the rest of the theory say?

I think you may have misplaced a minus sign.

Last edited: Feb 21, 2013
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