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"The potential V (volts) of points B with respect to point A is the work done against the field in taking a unit positive charge from A to B.

For a one-dimensional problem with A at [itex]x_0[/itex] and B at an arbitrary distance x, it follows that:

[tex]V = - \int_{x_0}^{x} E dx [/tex]

where E represents the X component of the field.

Differentiating the above equation we have: [tex]E = - \frac{dV}{dx}[/tex]

The minus sign shows that the electric field is directed from the region of higher potential to the region of lower potential."

I'm wondering if the above concepts (like the one regarding the direction of the electric field) hold in the following cases:

- the charge taken from A to B is an electron;

- the charge is an electron, plus A is grounded and B has a negative voltage;

Any help would be appreciated. Thanks in advance.