Question

what happens as you move them closer? further? how is potential energy connected to thermal energy? what does potential energy depend on?

Explanation:

Step1: Move charges closer

When you move two charges of the same sign closer in an electric - field, the electric potential energy increases because work is done against the electrostatic repulsion. Mathematically, for two point - charges $q_1$ and $q_2$ separated by a distance $r$, the electric potential energy $U = \frac{kq_1q_2}{r}$ (where $k$ is the Coulomb's constant). As $r$ decreases, $U$ increases.

Step2: Move charges further

When you move two charges of the same sign further apart, the electric potential energy decreases. Using the formula $U=\frac{kq_1q_2}{r}$, as $r$ increases, $U$ decreases.

Step3: Connection to thermal energy

Potential energy can be converted to thermal energy. For example, in a circuit with a resistor, the electric potential energy of the charges is converted into thermal energy (heat) as the charges flow through the resistor due to the resistance.

Step4: Dependence of potential energy

The electric potential energy of a system of charges depends on the magnitudes of the charges ($q_1$ and $q_2$) and the distance ($r$) between them as described by $U = \frac{kq_1q_2}{r}$. For gravitational potential energy near the Earth's surface, $U = mgh$ where $m$ is the mass, $g$ is the acceleration due to gravity and $h$ is the height. In general, potential energy depends on the position of an object in a force - field and the properties of the object (such as charge or mass).

Answer:

When moving charges closer (same - sign), potential energy increases; when moving them further, potential energy decreases. Potential energy can be converted to thermal energy. It depends on the properties of the object (charge or mass) and its position in a force - field.