Electric Potential Energy and Electric Potential
Electric potential energy and electric potential are fundamental concepts in understanding how charged particles interact.
Electric Potential Energy
Definition
Electric potential energy
Electric potential energy is the energy stored in a system of charged particles due to their positions relative to each other.
For two point charges, the electric potential energy is given by:
$$
E_p = \frac{k q_1 q_2}{r}
$$
where:
- $E_p$ is the electric potential energy.
- $k$ is the Coulomb constant ($8.99 \times 10^9 \, \text{N m}^2/ \text{C}^2$).
- $q_1$ and $q_2$ are the magnitudes of the charges.
- $r$ is the distance between the charges.
The formula resembles Coulomb’s law, but instead of force, it calculates energy.
Properties of Electric Potential Energy
- Scalar Quantity: Electric potential energy is a scalar, meaning it has magnitude but no direction.
- Depends on Charge Signs:
- If the charges are of opposite signs, the energy is negative, indicating an attractive interaction.
- If the charges have the same sign, the energy is positive, indicating a repulsive interaction.
- Reference Point: The reference point for electric potential energy is usually taken at infinity, where the energy is zero.
- Consider two charges,$q_1 = 2 \, \mu\text{C}$ and $q_2 = -3 \, \mu\text{C}$, separated by $0.05 \, \text{m}$.
- The electric potential energy is: $$
E_p = \frac{(8.99 \times 10^9) (2 \times 10^{-6})(-3 \times 10^{-6})}{0.05} = -1.08 \, \text{J}
$$ - The negative sign indicates an attractive interaction.
Electric Potential
Definition
Electric potential
Electric potential is the amount of work done per unit charge in bringing a small positive test charge from infinity to a point in an electric field.
It is defined as:
$$
V_e = \frac{k Q}{r}
$$
where:
- $V_e$ is the electric potential.
- $Q$ is the charge creating the potential.
- $r$ is the distance from the charge.
