College Physics B

Electric Forces Coulomb’s Law

Motion of Electric College Physics B - PHY2054C Charge Conductors Insulators Metals Static Electricity Electric Forces and Fields

Electric Field

Electric Flux Gauss’ Law

08/27/2014

My Office Hours: Tuesday 10:00 - 12:00 Noon 206 Keen Building College Physics B Outline

Electric Forces Coulomb’s Law 1 Electric Forces Motion of Electric Coulomb’s Law Charge Conductors Insulators Metals 2 Motion of Electric Charge Static Electricity Conductors Electric Field

Electric Flux Insulators Gauss’ Law Metals Static Electricity

3 Electric Field

4 Electric Flux Gauss’ Law College Physics B

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity Electric Field Discovery of electricity is generally credited to the Greeks. Electric Flux Gauss’ Law • About 2500 years ago: They observed electric charges and the forces between them in many situations. • Greeks used amber (a type of dried, hardened tree sap) and rubbed it with a piece of animal fur. ➜ Greek word for amber was electron. • The observed force even occurs when the amber (or plastic in the picture) and the paper are not in contact. College Physics B Electric Forces

Electric Forces Coulomb’s Law Electric force can be attractive or repulsive. Motion of • Electric It is extremely large. Charge Conductors Insulators Metals Static Electricity

Electric Field

Electric Flux Gauss’ Law College Physics B Electric Forces

Electric Forces Coulomb’s Law Electric force can be attractive or repulsive. Motion of • Electric It is extremely large. Charge • Conductors Assume two charged particles can be modeled Insulators Metals as point particles. Static Electricity

Electric Field

Electric Flux Gauss’ Law College Physics B Electric Forces

Electric Forces Coulomb’s Law Electric force can be attractive or repulsive. Motion of • Electric It is extremely large. Charge • Conductors The magnitude of the electric force between the Insulators Metals two particles is given by Coulomb’s Law. Static Electricity

Electric Field Electric Flux Direction of the force is along the Gauss’ Law line that connects the 2 charges. • A repulsive force will give a positive value for F. • An attractive force will give a negative value for F. • k = 8.99 × 109 N · m2/C2 “Coulomb constant” College Physics B Features of Coulomb’s Law

Electric Forces Coulomb’s Law Direction of the force Motion of • The product q · q determines the sign. Electric 1 2 Charge • Conductors For like charges, the product is positive. Insulators ➜ Metals The force tends to push the charges farther Static Electricity apart. Electric Field • Electric Flux For unlike charges, the product is negative. Gauss’ Law ➜ The charges are attracted to each other. College Physics B Features of Coulomb’s Law

Electric Forces Coulomb’s Law Direction of the force Motion of • The product q · q determines the sign. Electric 1 2 Charge • Conductors For like charges, the product is positive. Insulators ➜ Metals The force tends to push the charges farther Static Electricity apart. Electric Field • Electric Flux For unlike charges, the product is negative. Gauss’ Law ➜ The charges are attracted to each other.

The form of Coulomb’s Law is similar to Newton’s Law of Universal Gravitation:

q ·q · 1 2 F G m1 m2 F = k r 2 = r 2

r = distance between q1 and q2 or m1 and m2 attractive or repulsive always attractive! College Physics B Gravity

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity

Electric Field

Electric Flux Gauss’ Law

“Inverse-Square Law” College Physics B Gravity

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity

Electric Field

Electric Flux Gauss’ Law

“Inverse-Square Law” College Physics B Coulomb’s Law

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity

Electric Field

Electric Flux Gauss’ Law Every charged particle in the universe attracts (or repels) every other charged particle with a force that is directly proportional to the product of the charges of the particles and inversely proportional to the square of the distance between them.

Electric Field Hockey: phet.colorado.edu/en/simulation/electric-hockey College Physics B Coulomb’s Law

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity Electric Field Charles-Augustin de Coulomb Electric Flux (14 June 1736 - 23 August 1806) Gauss’ Law

q q F = k 1 2 r 2 1 k = = 8.99 × 109 N · m2/C2 4πǫ0

ǫ0 is called permittivity of free space College Physics B Example: Hydrogen Atom

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity

Electric Field

Electric Flux Gauss’ Law q · q −(1.6 × 10−19)2 F = k · proton electron = 8.99 × 109 · N r 2 (0.53 · 10−10)2 ≈− 8.2 × 10−8 N a = F/m ≈ 9.0 × 1022 m/s2

with r = 0.53−10 m. College Physics B Example: Helium Nucleus

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity

Electric Field

Electric Flux Gauss’ Law q · q (1.6 × 10−19)2 F = k · proton proton = 8.99 × 109 · N r 2 (10−15)2 ≈ + 230 N

with r = 10−15 m. College Physics B Size of the Electric Force

Electric Forces Coulomb’s Law Motion of Assume you have two boxes each containing 1 g of Electric Charge electrons: Conductors Insulators • × 27 Metals There would be 1.1 10 electrons in each box. Static Electricity • Electric Field The force between the two boxes would be about × 26 Electric Flux 3 10 N with the boxes separated by r = 1 m. Gauss’ Law ➜ This is almost a million times larger than the force between the Sun and the Earth. College Physics B Superposition of Forces

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity

Electric Field

Electric Flux Gauss’ Law

When there are more than two charges in a problem, the “Superposition Principle” must be used.

1 Find the forces on the charge of interest due to all the other forces. 2 Add the forces as vectors. F~ = F~1 + F~2 College Physics B Question

Electric Forces Two uniformly charged spheres are firmly fastened to Coulomb’s Law

Motion of and electrically insulated from frictionless pucks on an Electric Charge air table. The charge on sphere 2 is three times the Conductors Insulators charge on sphere 1. Which force diagram correctly Metals Static Electricity shows the magnitude and direction of the electrostatic Electric Field forces? Electric Flux Gauss’ Law

A C

B D College Physics B 1 Recognize the Principle • The electric force can be found using Coulomb’s Law. • Electric The principle of superposition may also be needed. Forces Coulomb’s Law 2 Sketch the Problem Motion of • Construct a drawing and show the location and charge of Electric Charge each object (include a coordinate system). Conductors • Insulators Include the directions of all electric forces acting on the Metals particle of interest. Static Electricity

Electric Field 3 Identify the Relationships Electric Flux • Use Coulomb’s Law to find the magnitude of the forces Gauss’ Law acting on the particle of interest. 4 Solve • The total force on a particle is the sum of all the forces. • Add the forces as vectors. • It is usually easier to work in terms of the components along the coordinate system. 5 Check • Consider what the answer means. • Check if the answer makes sense. College Physics B Outline

Electric Forces Coulomb’s Law 1 Electric Forces Motion of Electric Coulomb’s Law Charge Conductors Insulators Metals 2 Motion of Electric Charge Static Electricity Conductors Electric Field

Electric Flux Insulators Gauss’ Law Metals Static Electricity

3 Electric Field

4 Electric Flux Gauss’ Law College Physics B Structure of Matter

Electric Forces Coulomb’s Law ... from an “electrical” point of view: Motion of Electric • Conductors (copper, silver, gold, iron, lead, etc.) Charge Conductors are materials, in which electric charge can move freely. Insulators Metals • Insulators (glass, plastic, rubber, wood, etc.) Static Electricity

Electric Field do not allow charges to move. Electric Flux • Semiconductors (silicon, germanium, etc.) Gauss’ Law are materials, in which charges can move under the influence of small electrical forces. College Physics B Conductors

Electric Forces • Each atom by itself is Coulomb’s Law

Motion of electrically neutral. Electric ➜ Charge Equal numbers of Conductors Insulators protons and electrons Metals • Static Electricity When these atoms come Electric Field together to form the metal Electric Flux piece, electrons are freed. Gauss’ Law • The electrons move freely through the entire piece of metal leaving behind protons. ➜ Conduction Electrons

A piece of metal can also accept extra electrons or release some of its conduction electrons so that the entire object can acquire a net positive or negative charge. College Physics B Insulators

Electric Forces • In insulators, the electrons Coulomb’s Law

Motion of are not able to move freely Electric Charge through the material. Conductors • Insulators Examples include quartz, Metals Static Electricity plastic, and amber. Electric Field • Electrons cannot escape Electric Flux Gauss’ Law from these ions. • There are no conduction electrons available to carry charge through the solid. • If extra electrons are placed on an insulator, they tend to stay in that same place. College Physics B Excess Charge on a Metal

Electric Forces Coulomb’s Law • Electrons can move easily Motion of through a metal. Electric Charge • Conductors Excess electrons will be Insulators Metals distributed on the surface of Static Electricity the metal. Electric Field Electric Flux Why? Gauss’ Law College Physics B Excess Charge on a Metal

Electric Forces Coulomb’s Law • Electrons can move easily Motion of through a metal. Electric Charge • Conductors Excess electrons will be Insulators Metals distributed on the surface of Static Electricity the metal. Electric Field • Electric Flux Eventually, all the charge Gauss’ Law carriers will come to rest and be in static equilibrium. • For a metal in equilibrium: 1 Any excess electrons must be at the surface. 2 The electric field is zero inside metal in equilibrium. ➜ Faraday’s Cage College Physics B Faraday’s Cage

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity

Electric Field

Electric Flux Gauss’ Law College Physics B Faraday’s Cage

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity

Electric Field

Electric Flux Gauss’ Law College Physics B Faraday’s Cage

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity

Electric Field

Electric Flux Gauss’ Law College Physics B Charging an Object by Rubbing

Electric Forces Coulomb’s Law The act of rubbing causes some Motion of charge to be transferred from one Electric Charge material to another Conductors Insulators Metals Example: Static Electricity • Electric Field When rubbing amber with Electric Flux fur, electrons are moved Gauss’ Law from the fur to the amber. • The amber acquires a net negative charge. • The fur is left with a net positive charge.

Applies to many combinations of materials. phet.colorado.edu/en/simulation/travoltage College Physics B Polarization

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity

Electric Field

Electric Flux Gauss’ Law

Initially, the rod and the paper are both neutral. • The rod is rubbed by the fur, obtaining a negative charge. • The presence of the rod causes the electrons in the paper to be repelled and the positive ions are attracted. ➜ The paper is said to be polarized. College Physics B Polarization

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity

Electric Field

Electric Flux Gauss’ Law

The paper is electrically neutral. • The negative side of the paper is repelled. • The positive side of the paper is closer to the rod so it will experience a greater electric force. • The net effect is that the positive side of the paper is attracted to the negative side. College Physics B Polarization

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity

Electric Field

Electric Flux Gauss’ Law

Balloons and Static Electricity: phet.colorado.edu/en/simulation/balloons College Physics B Outline

Electric Forces Coulomb’s Law 1 Electric Forces Motion of Electric Coulomb’s Law Charge Conductors Insulators Metals 2 Motion of Electric Charge Static Electricity Conductors Electric Field

Electric Flux Insulators Gauss’ Law Metals Static Electricity

3 Electric Field

4 Electric Flux Gauss’ Law College Physics B Electric Field

Electric Forces An electric field gives another explanation of electric forces. Coulomb’s Law

Motion of Electric The presence of a charge produces an electric field: Charge Conductors Insulators Metals Static Electricity

Electric Field

Electric Flux Gauss’ Law College Physics B Electric Field

Electric Forces An electric field gives another explanation of electric forces. Coulomb’s Law

Motion of Electric The presence of a charge produces an electric field: Charge Conductors Insulators • A positive charge produces field Metals Static Electricity lines that radiate outward. Electric Field • For a negative charge, the field Electric Flux Gauss’ Law lines are directed inward, toward the charge. • The electric field is a vector and denoted by E~ . • The density of the field lines is proportional to the magnitude of E. ➜ The field lines are most dense in the vicinity of charges. College Physics B Electric Field

Electric Forces The Electric Field is defined as the force exerted on a tiny Coulomb’s Law

Motion of positive test charge at that point divided by the magnitude Electric Charge of the test charge: Conductors Insulators • Consider a point in space where Metals Static Electricity the electric field is E. Electric Field • If a charge q is placed at the point, Electric Flux Gauss’ Law the force is given by F = q E. • The charge q is called a test charge. • By measuring the force on the test charge, the magnitude and direction of the electric field can be inferred. College Physics B Electric Field

Electric Forces The Electric Field is defined as the force exerted on a tiny Coulomb’s Law

Motion of positive test charge at that point divided by the magnitude Electric Charge of the test charge: Conductors Insulators • Consider a point in space where Metals Static Electricity the electric field is E. Electric Field • If a charge q is placed at the point, Electric Flux Gauss’ Law the force is given by F = q E. • Unit of the electric field is N/C:

Qq F = k = q E r 2 Q E = k r 2 College Physics B Electric Fields are Vectors

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity

Electric Field

Electric Flux Gauss’ Law College Physics B Rules for Drawing Field Lines

Electric Forces The lines must begin on a positive charge and terminate on a Coulomb’s Law

Motion of negative charge (or at infinity). Electric Charge • The number of lines drawn leaving a positive charge or Conductors Insulators approaching a negative charge is proportional to the Metals Static Electricity magnitude of the charge. Electric Field • No lines can cross. Electric Flux Gauss’ Law College Physics B Outline

Electric Forces Coulomb’s Law 1 Electric Forces Motion of Electric Coulomb’s Law Charge Conductors Insulators Metals 2 Motion of Electric Charge Static Electricity Conductors Electric Field

Electric Flux Insulators Gauss’ Law Metals Static Electricity

3 Electric Field

4 Electric Flux Gauss’ Law College Physics B Electric Flux

Electric Forces Coulomb’s Law Gauss’ Law can be used to find the electric field of a com- Motion of plex charge distribution. Electric Charge Conductors • Easier than treating it as a collection of point charges Insulators Metals and using superposition. Static Electricity

Electric Field Electric Flux To use Gauss’ Law, a quantity called the Electric Flux is Gauss’ Law needed. • The electric flux is equal to the number of electric field lines that pass through a particular surface multiplied by the area of the surface. • The electric flux is denoted by ΦE = E A. College Physics B Electric Flux: Examples

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity

Electric Field Electric Flux A The electric field is perpendicular to the surface of A: Gauss’ Law ➜ ΦE = E A B The electric field is parallel to the surface of A: ➜ ΦE = E A = 0 College Physics B Electric Flux: Examples

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity

Electric Field Electric Flux A The electric field is perpendicular to the surface of A: Gauss’ Law ➜ ΦE = E A B The electric field is parallel to the surface of A: ➜ ΦE = E A = 0 C The electric field forms an angle with the surface A: ➜ ΦE = E A cos Θ College Physics B Electric Flux: Examples

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity

Electric Field Electric Flux A The electric field is perpendicular to the surface of A: Gauss’ Law ➜ ΦE = E A B The electric field is parallel to the surface of A: ➜ ΦE = E A = 0 C The electric field forms an angle with the surface A: ➜ ΦE = E A cos Θ D The flux is positive if the field is directed out of the region surrounded by the surface and negative if going into the region: ΦE = 0 College Physics B Gauss’ Law

Electric Forces Coulomb’s Law

Motion of Electric Charge Conductors Insulators Metals Static Electricity Electric Field Carl Friedrich Gauss Electric Flux (30 April 1777 - 23 February 1855) Gauss’ Law

Gauss’ Law says that the electric flux through any closed surface is proportional to the charge Q inside the surface:

Q ΦE = ǫ0

ǫ0 is called permittivity of free space College Physics B Field of a Point Charge

Electric Forces Choose a Gaussian surface Coulomb’s Law Motion of • Choose a surface that will make the calculation easy. Electric Charge • Conductors Surface should match the symmetry of the problem. Insulators ➜ Metals For a point charge, the field lines have a spherical Static Electricity symmetry. Electric Field • Electric Flux The spherical symmetry means that Gauss’ Law the magnitude of the electric field depends only on the distance from the charge. • The magnitude of the field is the same at all points on the surface (due to the symmetry). • The field is perpendicular to the sphere at all points. College Physics B Field of a Point Charge

Electric Forces Choose a Gaussian surface Coulomb’s Law Motion of • Choose a surface that will make the calculation easy. Electric Charge • Conductors Surface should match the symmetry of the problem. Insulators ➜ Metals For a point charge, the field lines have a spherical Static Electricity symmetry. Electric Field

Electric Flux Gauss’ Law ΦE = E A sphere = E 4πr 2

= q/ǫ0

q → ′ E = 2 Coulomb s Law 4πǫ0 r College Physics B Problem Solving Strategy

Electric Forces 1 Recognize the Principle Coulomb’s Law • Motion of Calculate the electric flux through a Gaussian surface. Electric • The choice of the Gaussian surface is key! Charge Conductors 2 Sketch the Problem Insulators Metals • Draw the charge distribution. Static Electricity • Use symmetry of distribution to sketch the electric field. Electric Field • The Gaussian surface should match the symmetry of the Electric Flux Gauss’ Law electric field. 3 Identify the Relationships • Your Gaussian surface should satisfy one or more of the following conditions: • The field has constant magnitude over all or much of the surface and makes a constant angle with the surface. • The field may be zero over a portion of the surface. ➜ The flux through that part of the surface is zero. • The field may be parallel to some part of the surface. ➜ The flux through that part of the surface is zero. College Physics B Problem Solving Strategy

Electric Forces Solve Coulomb’s Law • Calculate the total electric flux through the entire Motion of Electric Gaussian surface. Charge • Conductors Find the total electric charge inside the surface. Insulators • Metals Apply Gauss’ Law to solve for the electric field. Static Electricity Check Electric Field • Consider what the answer means. Electric Flux • Gauss’ Law Check if the answer makes sense.