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Voltage in Electrical Systems 1.3.1

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Objectives Explain the similarities and differences between Newton’s law of universal gravitation and Coulomb’s law. Explain how force between two like charges and the force between two unlike charges are different. Describe how to create an electric field and interpret the information given in a drawing of an electric field.

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Universal Forces Include: gravitational and electrical –Gravitational force acts between two or more masses –Electrical force acts between two or more charges Called universal because each force behaves the same anywhere in the observable universe. The two forces are field forces and act over a distance (the masses or charges do not have to be touching – example – gravitational forces affect the earth and the moon or magnetic forces affecting two magnets).

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Gravitational Force Why cover gravitational force? 17 th century, Isaac Newton. View video clip (control+click)View video clip Newton’s universal law of gravitation –Every object in the universe attracts every other object with a force that is directly proportional to the mass of each body and inversely proportional to the square of the distance between them.

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Formula for Gravitational Force G = universal gravitational constant = 6.67 x Nm 2 /kg 2 m 1 = mass of first body in kilograms m 2 = mass of second body in kilograms d = distance between the two bodies in meters Fg = the gravitational force in Newtons

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Using the formula for gravitational forces Use the standard procedure of writing down the givens, solving for and formulas needed Convert masses to kilograms and distance to meters Write down the formula Rearrange the formula if necessary to solve for needed component If you are solving for Fg and set up the problem correctly you will be able to m2 from the distance and kg2 from the masses and then cancel out the m 2 and the kg 2 with those in G (Nm2/kg2)so that your remaining unit is N (Newton) which is the correct unit of force.

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Notes on numbers with exponents: When you multiple number with exponents : 1. multiply the numbers together as usual 2.add the exponents together – two positive exponents give you a larger positive exponent – two negative exponents give you a larger negative exponent - when exponents are of different signs you find the difference between them and give the sign of the larger exponent. When you have numbers with exponents in the numerator and denominator 1.Divide the numerator by the denominator 2.Subtract the exponent value in the denominator from the exponent value in the numerator

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If you are solving for Fg and set up the problem correctly you will be able to calculate m 2 from the distance and kg 2 from the masses cancel out the m 2 and the kg 2 with those in G (N · m 2 ) kg 2 Your remaining unit is N (Newton) which is the correct unit of force. Formula for Fg

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Set up the problem and solve. Use our standard procedure and the notes from slides (I will check your work in class when I check your notes.) Check your answer by sliding the brown box away from example 1.11.

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Electric Charge Electrostatic forces, the comb and the CRT. Charge – property of and object that causes electrical force. Two types of charge: positive and negative Electrical forces are either attractive or repulsive. –Like charges repel –Opposite charges attract.

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Origin of Charge Structure of atom. Charge of electron is equal in magnitude to proton but opposite in sign. Normal atom is neutral because number of protons and electrons are equal.

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Origin of Charge Charge can transferred –Comb example –Balloon example (in class) Principle of conservation of charge – net charge in an isolated system never changes. Net Charge = #protons – #electrons

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Electrical Force In 18 th century, French scientist Charles Coulomb discovered the relationship between force, charge and distance. Coulomb’s law –The electrical force between two charged bodies is directly proportional to the charge on each body and inversely proportional to the square of the distance between them.

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Electrical Force SI unit for charge is the Coulomb (C). Elementary charge of one electron or proton is 1.60 x C q 1 and q 2 are the charges on two objects. d = distance between charged objects K = constant = 9.0 x 10 9 Nm 2 /C 2

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Electrical Force Coulomb’s law similar to Newton’s universal law of gravitation. –But, gravitational force is always attractive. –Direction for electrical force depends on charge of particles.

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Set up the problem and solve. Use our standard procedure and the notes from slides (I will check your work in class when I check your notes.) Check your answer by sliding the brown box away from example Example 1.12 is on the next slide

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Scale and Universal Forces Small distance and mass as in atoms, electrical forces are important and gravitational force is insignificant. Large distance and mass, significance reverses. Thus –Electrical forces govern the structure of atoms, molecules, solids, liquids and gases. –Gravitational forces govern the structure of planets, stars, galaxies and the universe.

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Gravitational and Electrical Fields Field forces are alterations in space around the body creating the field. –They are models used by scientists to help them understand and predict how forces are transmitted from one object to another. The field forces are vector quantities.

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Gravitational Field

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Electrical Field What happens when you substitute the respective laws into each equation above? E does not depend on size of test charge. g does not depend on size of test mass.

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Field Line Diagrams Illustration of a field can be done with field lines. Direction of field at any given point is tangent. Lines are close, field is strong Lines are far apart, field is weak

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Forces, units and Formulas Gravitational Field Electrical Field SI unit for charge is the Coulomb (C). Elementary charge of one electron or proton is 1.60 x C q 1 and q 2 are the charges on two objects. d = distance between charged objects K = constant = 9.0 x 10 9 Nm 2 /C 2 Electrical force Gravitational force G = universal gravitational constant = 6.67 x Nm 2 /kg 2 m 1 = mass of first body in kilograms m 2 = mass of second body in kilograms d = distance between the two bodies in meters Fg = the gravitational force in Newtons

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