# Electric Potential, Energy, and Capacitance

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Electric Potential, Energy, and Capacitance
Objective: TSW understand, transfer and apply energy concepts to electric fields and charges by solving problems involving electric fields and forces.

Let’s revisit energy concepts for a gravitational field
Let’s revisit energy concepts for a gravitational field. A 250 gram baseball is thrown upward with an initial velocity of 25m/s. What is the maximum height reached by the ball? EARTH v = 25m/s v = 0m/s

Let’s make a parallel comparison of Gravitational Potential Energy (Ug) to Electric Potential Energy (UE). Units: Units:

Now we will do an example:
An electron is released from rest in an electric field of 2000N/C. How fast will the electron be moving after traveling 30cm? _ v = 0m/s _ v = ? 30cm

A new quantity is defined called the Electric Potential Difference
A new quantity is defined called the Electric Potential Difference. It is the Electric Potential Energy per unit Charge. The Electric Potential Difference can be considered to be the electric “push” motivating a charge to move from one point to another. It is independent of the size of the charge. The Electric Potential Difference can also called the Electric Potential, the Potential, or the voltage. Units: Remember Energy and voltage are scalars, so you don’t have to deal with vectors (direction)

The electric potential energy can now be written in terms of the electric potential.

Let’s do an example using this new concept:
The potential difference between to charge plates is 500V. Find the velocity of a proton if it is accelerated from rest from one plate to the other. High Potential Low Potential 500V + - Positive charges move from high to low potential Negative charges move from low to high potential

Let’s revisit a gravitational field again:
The gravitational potential energy if the field is constant is given by: But, what if the field is not constant. In other words the gravitational potential energy of a mass located far away from the earth.

The gravitational potential energy of mass m is given by:
Notice r is not squared The gravitational potential energy at infinity is zero

Let’s us this new equation to do an example:
With what velocity must a rocket be fired in order to escape the earth’s gravitational field? (Neglect air resistance)

Let’s make a parallel comparison of Gravitational Potential Energy (Ug) to Electric Potential Energy (UE) when dealing with individual masses or charges. The gravitational potential energy between two masses is given by: The electric potential energy between two masses is given by:

Example: Two 40 gram masses each with a charge of -6µC are 20cm apart. If the two charges are released, how fast will they be moving when they are a very, very long way apart. (infinity)

Let’s use the electric potential energy between two charges to derive an equation for the electric potential (voltage) due to a single point charge. The electric potential energy is given by: q2 P r Let’s remove charge q2 and consider the electric potential (voltage) at point P. q1 To find the potential due to more than one point charge simply add up all the individual potentials:

What is the potential difference between the two levels?
Example 1: The electron in the Bohr model of the atom can exist at only certain orbits. The smallest has a radius of .0529nm, and the next level has a radius of .212m. What is the potential difference between the two levels? Which level has a higher potential? +e r1 r2 r1 is at a higher potential.

What is the electric potential at the center of the square?
Example 2 What is the electric potential at the center of the square? 45º r

Example 3: A proton is moved from the negative plate to the positive plate of a parallel-plate arrangement. The plates are 1.5cm apart, and the electric field is uniform with a magnitude of 1500N/C. How much work would be required to move a proton from the negative to the positive plate? What is the potential difference between the plates? If the proton is released from rest at the positive plate, what speed will it have just before it hits the negative plate? 1

Example 3: A proton is moved from the negative plate to the positive plate of a parallel-plate arrangement. The plates are 1.5cm apart, and the electric field is uniform with a magnitude of 1500N/C. b) What is the potential difference between the plates?

Example 3: A proton is moved from the negative plate to the positive plate of a parallel-plate arrangement. The plates are 1.5cm apart, and the electric field is uniform with a magnitude of 1500N/C. c) If the proton is released from rest at the positive plate, what speed will it have just before it hits the negative plate? Use conservation of energy

Example 4: Compute the energy necessary to bring together the charges in the configuration shown below: Calculate the electric potential energy between each pair of charges and add them together.

Capacitors Two parallel conducting plates used to store charge, which in turn stores energy

Charge flows through the circuit until the capacitor is charge at which point no more charge flows.

The amount of charge stored per volt of potential difference.
Capacitance The amount of charge stored per volt of potential difference. C = Capacitance (C/V = Farad (F). Q = The stored charge (C). V = The potential difference (voltage) between the plates (V).

Capacitance based on the physical characteristics of the capacitor
Є0 = Permittivity of free space = 8.85 x 10-12 A = Surface area of one plate. d = distance between plates.

Example 1: Find the Charge stored in the capacitor.
12V 20μF

Capacitors in Series

Example 2: Find the total charge stored in each the capacitor.
Now find the total charge First calculate the total capacitance. 12V 10μF 20μF 30μF In a series circuit the charge stored on each capacitor is the same and the voltage is split.

Capacitors in Parallel

Example 3: Find the total charge stored in all the capacitors.
Now calculate the total charge. First find the total capacitance. 12V 10μF 20μF 30μF In a parallel circuit the charge stored on each capacitor can be different and the voltage must be the same.

Example 4: Find the total capacitance of all the capacitors.
First find the total capacitance of the parallel capacitors 12V 12μF 8μF 4μF Now, combine this value in series with 12μF capacitor.

Energy Stored in a Capacitor
Units: Joules (J)