# Electric Potential Energy

When an object was lifted against gravity by applying a force for some distance, work was done to give that object gravitational potential energy

When a charged object is moved against an electric field by applying a force for some distance, work is done to give that object electric potential energy.

The work done per unit charge in moving a charge between two points in an electric field is a scalar known as the electric potential V (or voltage)

Units: volts (1V = 1 J/C)

The work done is equal to the change in the object's electric potential energy (U

_{E})

# The Electron-Volt

Oftentimes the electrical energy and/or work done is a very small portion of a joule

A smaller, alternative, non-standard unit of energy is often used for convenience, known as the electron volt (eV)

1 eV is the amount of work done in moving an elementary charge through a potential difference of 1 volt

# Equipotential Lines

Topographic maps show you lines of equal altitude, or equal gravitational potential

Lines connecting points of equal electrical potential are known as equipotential lines.

Equipotential lines always cross electrical field lines at right angles

If you move a charged particle in space, and stay on an equipotential line, no work will be done.

As equipotential lines get closer together, the gradients of the potential increases (stepper "slope" of potentials)

Electric field points from high to low potential

# Electric Potential Energy Due to a Point Charge

# Electric Force from Electric Potential Energy

# Electric Potential Due to a Point Charge

Electric potential (voltage) is the work per unit charge required to bring a charge from infinity to some point R in an electric field

# Example 1: Electric Potential Due to a Point Charge

Find the electric potential at point P, located 3 meters away from a -2 C charge.

What is the electric potential energy of a 0.5 C charge situated at point P?

# Example 2: Electric Potential Due to a Point Charge

Find the electric potential at the origin due to the three charges shown in the diagram. If an electron is placed at the origin, what potential energy does it possess?

# Finding Electric Field from Electric Potential

# Finding Electric Potential from Electric Field

# Example 3: Electric Potential Due to a Point Charges

# Example 4: Electric Field from Potential

# Example 5: Speed of an Electron Released in an Electric Field

# Example 6: Work Required to Establish a Charge System

![Two point charges (5 VLC and 2 [LC) are placed 0.5 meters apart. How much work was required to establish the charge system? ](./media/image103.png)

# 2013 Free Response Question 1

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# 2006 Free Response Question 1

# 2005 Free Response Question 1

# 2003 Free Response Question 1