Electric Forces, Fields, Potential and Energy

Fundamental Charge: The charge on one electron. e = 1.6 x C Unit of charge is a Coulomb (C)

Two types of charge: Positive Charge: A shortage of electrons. Negative Charge: An excess of electrons. Conservation of charge – The net charge of a closed system remains constant.

+ n n n n n n Neutral Atom Number of electrons = Number of protons Nucleus Negative Atom Number of electrons > Number of protons -2e = -3.2 x C - - Positive Atom Number of electrons < Number of protons +2e = +3.2 x C

Electric Forces Like Charges - Repel Unlike Charges - Attract - + F F + + F F

Coulombs Law – Gives the electric force between two point charges. k = Coulombs Constant = 9.0x10 9 Nm 2 /C 2 q 1 = charge on mass 1 q 2 = charge on mass 2 r = the distance between the two charges The electric force is much stronger than the gravitational force. Inverse Square Law

If r is doubled then F is : If q 1 is doubled then F is : If q 1 and q 2 are doubled and r is halved then F is : ¼ of F 2F 16F Two charges are separated by a distance r and have a force F on each other. q1q1 q2q2 r F F Example 1

Example 2 Two 40 gram masses each with a charge of 3μC are placed 50cm apart. Compare the gravitational force between the two masses to the electric force between the two masses. (Ignore the force of the earth on the two masses) 3μC 40g 50cm 3μC 40g

The electric force is much greater than the gravitational force

5μC5μC - 5μC Three charged objects are placed as shown. Find the net force on the object with the charge of -4μC. - 4μC F2F2 F1F1 F 1 and F 2 must be added together as vectors. 20cm 45º Example 3

F1F1 F2F2 45º 2.3cos sin451.6 F 1 = F 2 = + F net = θ 3.31N at 209º 29º

Example 4 Two 8 gram, equally charged balls are suspended on earth as shown in the diagram below. Find the charge on each ball. q q 20º L = 30cm FEFE FEFE r =2(30sin10º)=10.4cm 10º 30sin10º r

Draw a force diagram for one charge and treat as an equilibrium problem. FEFE F g =.08N T q Tsin80º Tcos80º 80º

Electric Fields: A property of space around a charge that causes forces on other charges. The force per unit charge felt by a positive test charge placed in the field _ + FEFE + FEFE + FEFE Use a positive test charge

+ + FEFE + FEFE + FEFE

The gravitational Force = (The mass) x (The Gravitational Field) The units for a gravitational field are N/kg The Electric Force = (The charge) x (The Electric Field) The units for a electric field are N/C

Things to Know Electric field lines go out of a positive charge and into a negative charge. Positive charges experience a force with the field. Negative charges experience a force against the field. The Electric Field inside a conductor is zero.

Example 3 What is the electric field at a point 25cm away from a point charge of 2µC? 2µC 25cm Away from the charge E

Example 4 A 5 gram mass with a charge of -3µC is released from rest in a constant field of 20000N/C directed in the positive x direction. Find its position and velocity after 4.0 seconds. 5g -3µC F E = qE Negative charges experience a force against the field

Example 6 What is the electric field at the origin? The electric field due to each charge must be calculated individually and then added together as vectors. E1E1 To the right (+) E2E2 E3E3 Up (+)

Now add the vectors together: E 1 =735N/C E 2 =720N/C E 3 =844N/C E 1 = E 3 = E 2 = E = 1455N/C 844N/C E θ

The electric field due to more than one point charge. + F - F

Two charged parallel plates The Electric field is constant between the two plates.

The Electric Field inside a conductor is zero E = 0N/C

An electron has a velocity of 6x10 5 m/s as it enters a constant electric field of 10000N/C as shown in the diagram below. How far will the electron travel in the x direction before striking one of the plates? 4cm _ v First the force and acceleration of the electron must be calculated. Now we have a simple projectile motion problem! The Electron will follow a parabolic path as shown 2.82 x m

Lets make a parallel comparison of Gravitational Potential Energy (U g ) to Electric Potential Energy (U E ). Units: The Electric Potential Energy at a point is the work done to move a charge from infinity to that point.

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. It is the work done per unit charge to move a small positive test charge between two points. Units: The Electric Potential Difference can also called the Electric Potential, the Potential, or the voltage. Remember Energy and voltage are scalars, so you dont have to deal with vectors (direction)

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

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

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)

Lets use the electric potential energy between two charges to derive an equation for the electric potential (voltage) due to a single point charge. q1q1 q2q2 r The electric potential energy is given by: Lets remove charge q 2 and consider the electric potential (voltage) at point P. P To find the potential due to more than one point charge simply add up all the individual potentials:

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.212nm. a)What is the potential difference between the two levels? b)Which level has a higher potential? +e r1r1 r2r2 r 1 is at a higher potential.

Example 2 What is the electric potential at the center of the square? 45º r r r 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. a)How much work would be required to move a proton from the negative to the positive plate? b)What is the potential difference between the plates? c)If the proton is released from rest at the positive plate, what speed will it have just before it hits the negative plate?

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.