Fields

Objects with mass

Objects with charge

$G$ is a physical constant

Note: ${\epsilon }_0$ is a physical constant

$$\left[g\right]=N{\mathrm{kg}}^{-1}=m{s}^{-2}$$

$g$ is a vector and is the graviational field strength.

$$\left[E\right]=N{C}^{-1}=V{m}^{-1}$$

$E$ is a vector and is the electric field strength.

Force per unit mass $$g=\frac{F}{m}$$

$m$ is a test small test mass.

Force per unit charge $$E=\frac{F}{Q}$$

$Q$ is a test small test charge.

Always attractive

This is a vector

Can be attractive or repulsive

This is a vector

$$V=-\frac{Gm}{r}$$ Jkg^-1

Scalar

Always less than zero.

$$V=\frac{kQ}{r}$$ JC^-1

Scalar

Sign depends on charges

Work done in bringing a unit mass from infinity to the point in the field.

Work done in bringing a unit positive charge from infinity to the point in the field.