Understanding Electric Potential: Work and Infinity Explained

[v_pino]

I've been told that Electric potential (V) is the work done in bringing a point charge (+1C) from infinity to a given point in an electric field.

Why infinity? And how come it is negative?

What should I research into for further details?

Thank you.

 

[nicksauce]

Potentials are always defined up to a constant. That means that there needs to be some reference point to uniquely define the potential. Sort of like defining altitude relative to sea level. It is conventional to choose infinity as the reference point, since electric fields are generally 0 at infinity, and it greatly simplifies the math.

The negative sign is because it is conventional to write
$$\vec{F} = -\nabla\phi$$
where F is the force and phi is the potential energy.
This extends to electrostatics, so we write
$$\vec{E} = -\nabla V$$