# Electrical Charge Electrical Force and Electric Fields Electrical

• Slides: 30

Electrical Charge, Electrical Force, and Electric Fields

Electrical Charge • All atoms have a positively charged nucleus made of protons (+) and neutrons (0) that are surrounded by electrons (-) • When the positive charge equals the negative charge the atom is neutral. • When an object gains electrons, the object becomes negatively charged. When an object loses electrons, the object becomes positively charged. • Electrical charge is all about electrons!!

Electrical Charge Facts • Like charges repel one another while unlike charges attract • When you rub a balloon across your hair, the charge on your hair is positive (lost electrons) while the charge on the balloon is negative (gained electrons). • Electric charge is always conserved (not created or destroyed)

Electrical Charge Facts • The standard unit for electrical charge is the Coulomb (C) • The magnitude of the charge on one electron and on one proton is 1. 60 X 10 -19 C. The charges have opposite signs. • e is ‘elemental charge’ - 1. 60 X 10 -19 C Millikan’s Oil Drop Experiment in 1909

Electrical Insulators (dielectrics) & Conductors • An insulator, aka dielectric, is a material that does not transfer charge easily; insulators have tightly bound electrons. Charge is redistributed. • Ex: glass, wood, dry air, most plastics • A conductor is a material that transfers charge easily; conductors have loosely bound electrons • Ex: most metals, water, human body

Dielectrics • Plastic, glass, and other nonmetal materials do not have free electrons or any other charged particles that are free to move inside. © 2014 Pearson Education, Inc.

Electrical Insulators & Conductors • Charges added to one part of an insulator remain on that part whereas charges added to a conductor quickly spread over the surface of the object. • Although air is an insulator, in certain conditions it can also become a conductor.

Grounding • Eliminating excess charge by touching a charged object like the wiring in your house to the earth. Earth is so massive, the charge dissipates very rapidly. • Lightning rods bring excess charge to the ground.

Charging a Neutral Object • Conduction – charging a neutral object by touching it with a charged object • Induction – charging a neutral object by separating the charges and then grounding the object

Coulomb's force law • In 1785, Charles Coulomb determined the relationship between distance and magnitude of charges, and the force between charges. • The experimental apparatus Coulomb used is called a torsion balance. © 2014 Pearson Education, Inc.

Coulomb’s Law Experiment shows that the electric force between two charges is proportional to the product of the charges and inversely proportional to the distance between them. Inverse square Law like Gravity 11

Coulomb’s Law Coulomb’s law: Where Q 1 and Q 2 are the amount of charge and k is a proportionality constant Charges produced by rubbing ordinary objects (such as a comb or a plastic ruler) are typically around a microcoulomb or less: 12

Coulomb’s Law The charges carried by the proton and electron are equal in size. However, the mass of the proton is 2000 times the mass of the electron. 13

Coulomb’s Law and Elemental Charge The magnitude of the charge of an electron, on the other hand, has been determined to be about 1. 602 x 10 -19 C, and its sign is negative. This is the smallest known charge, and because of its fundamental nature, it is given the symbol e and is often referred to as the elementary charge: Example: How many electrons make up a charge of -30. 0 micro coulombs ( C)? N = Q/e = (-30 x 10 -6 C)/ (-1. 60 x 10 -19 C/electrons) = 1. 88 x 1014 electrons What is the mass of 1. 88 x 1014 electrons? Mass = (9. 11 x 10 -31 kg)(1. 88 x 1014 electrons) = 1. 71 x 10 -16 kg 14

Coulomb’s Law • Double one of the charges – force doubles • Change sign of one of the charges – force changes direction • Change sign of both charges – force stays the same • Double the distance between charges – force four times weaker • Double both charges – force four times stronger 15

Coulomb’s Law • • FElectric = k q. A q. B d 2 • FElectric = Electric Force (Newtons) • k = 8. 988 x 109 Nm 2/C 2 • q. A = charge A ( C) q. B = charge B (C) • d = distance between A and B (meters)

Coulomb’s Law vs. Law of Universal Gravitation • F = k. Q 1 Q 2/r 2 vs. F=GM 1 M 2/r 2 • Both are inverse square laws F 1/r 2 • Both have a proportionality to a product of each bodymass for gravity, electric charge for electricity. • A major difference is that gravity is always an attractive force, whereas the electric force can be wither attractive or repulsive. • Electrical Force is stronger than gravitational force 17

Solving Problems involving Coulomb’s Law Sample problem Find the force between two positive 1. 0 C charges when they are 1000 m apart? Solution q 1=q 2 = 1. 0 C r = 1000 m k = 9. 0 x 109 Nm 2/C 2 F = kq 1 q 2/r 2 F= (9. 0 x 109 Nm 2/C 2) (1. 0 C) (1000 m)2 F = 9. 0 x 103 N 18

Solving Problems involving Coulomb’s Law Sample problem What is the magnitude of the electric force of attraction between an iron nucleus (q = +26 e) and its innermost electron if the distance between them is 1. 5 x 10 -12 m? Solution q 1= 26 x 1. 6 x 10 -19 C q 2=-1. 6 x 10 -19 C k = 9. 0 x 109 Nm 2/C 2 F = kq 1 q 2/r 2 F = (9. 0 x 109 Nm 2/C 2)[(26)(1. 6 x 10 -19 C)](-1. 6 x 10 -19 C) (1. 5 x 10 -12 m)2 F = -2. 7 x 10 -3 N 19

Solving Problems involving Coulomb’s Law Sample problem What is the repulsive electrical force between two protons in a nucleus that are 5. 0 x 10 -15 m apart from each other? Solution k = 9. 0 x 109 Nm 2/C 2 q= +1. 6 x 10 -19 C r= 5. 0 x 10 -15 m F = kq 1 q 2/r 2 F = (9. 0 x 109 Nm 2/C 2)(1. 6 x 10 -19 C) (5. 0 x 10 -15 m)2 F = 9. 2 N 20

Electric Fields • An electric field is a region around a charged object in which a stationary charged object experiences an electric force. • An electric field is in all directions (3 D). • Direction of the electric field is the direction in which a force would act on a positive charge.

Electric Fields Electric field lines represent both magnitude and direction of the electric field.

Electric Potential/Potential Difference • Electric potential is energy associated with a charged particle due to its position relative to a source of electric force. • Electric potential difference (ΔV) is the change in electrical energy divided by charge. • ΔV = E/q Unit is the Volt (1 J/C) • Potential difference between the two terminals of a battery can range from 1. 5 V to 12 V.

Potential Difference in a Uniform Field • ΔV = Ed ΔV = Potential Difference (volts) E = Intensity of Electric Field (N/C) D = distance (m) • Two parallel plates are given opposite charges that yields an electric potential difference of 60. 0 V. If the plates are 3 cm apart, what is the magnitude of the electric field? • ΔV = Ed E = ΔV/d • E = 60/. 03 = 2000 N/C

Charge Movement • Charges will move in conductors until the electric potential is the same everywhere on the conductor. • Charges move from higher potential to lower potential until they are equal. • Grounding eliminates excess charge by touching a charged object like the wiring in your house to the earth.

Basic Circuits

Basic Circuits • A circuit has to be a closed path for electric current to flow. • • V = IR V = Voltage (volts) V I = Current (amps) A R = Resistance (ohms) Ω

Basic Circuits • • • Ohm’s Law I = V/R V = Potential Difference or Voltage (volts) V I = Electric current (amps) A R = Resistance (ohms) Ω

Basic Circuits • A light bulb of 5 -Ω resistance is connected across a potential difference of 12 V. What is the current in the bulb? • I = V/R • I = 12/5 = 2. 4 amps

3 Charges d = 2 m West q 1 q 2 q 3 q 1 = + 2 X 10 -6 C q 2 = - 2 X 10 -6 C q 3 = - 3 X 10 -6 C • • d = 1 m East Fnet 2 = ?