Electric potential and electric potential energy help us understand how charges interact in an electric field. These are scalar quantities related to the work done by or against electric forces.

Electric Potential Energy (\( U \))

Electric potential energy is the energy a charged object possesses due to its position in an electric field.

For a charge \( q \) in the electric field of another point charge \( Q \), the potential energy is given by:

\[ U = k \frac{qQ}{r} \]

Where:

• \( U \): Electric potential energy (J)
• \( q, Q \): Charges involved (C)
• \( r \): Distance between the charges (m)
• \( k \): Coulomb’s constant \( \left( 8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2 \right) \)

Electric Potential (\( V \))

Electric potential at a point is the electric potential energy per unit charge at that point. It is defined as:

\[ V = \frac{U}{q} \]

In terms of point charges:

\[ V = k \frac{Q}{r} \]

Where \( V \) is the electric potential (in volts, V) at a distance \( r \) from a charge \( Q \).

Key Points

• Electric potential is a scalar quantity.
• It can be **positive or negative, depending on the sign of the source charge.
• The potential due to multiple charges is the algebraic sum of the potentials from each charge.
• Work done in moving a charge from one point to another is related to the potential difference \( \Delta V \):

\[ W = q \cdot \Delta V \]

Example: Work Done Moving a Charge

Written by Mubarak Aouda