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What is Electricity? zFlow of electrons. zElectromagnetic force

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BASIC MODEL

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Charge: Modern view charge comes in two flavors (positive and negative) normally balanced (neutral) the amount of positive charge in an object is fixed! imbalance causes “charge”

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Problem: A bushel basket contains 50 apples. How much of a bushel is just one apple?

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Measuring charge we measure in units called Coulombs (C) 6.25x10 18 bare protons is required to make 1C. What is the charge on a single proton?

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elementary charge we define the charge on one proton e=1.6 x10 -19 C the charge on the electron is then -e

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Problem A penny contains about 2 x10 23 protons and an equal number of electrons. If the penny is charged to +1C, what fraction of the electrons have been added or removed? fraction removed = #removed original #

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Problem A penny contains about 2 x10 23 protons and an equal number of electrons. If the penny is charged to +1C, what fraction of the electrons have been added or removed? fraction removed = #removed 2 x 10 23

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Problem A penny contains about 2 x10 23 protons and an equal number of electrons. If the penny is charged to +1C, what fraction of the electrons have been added or removed? fraction removed = 6.25 x 10 18 2 x 10 23

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Problem A penny contains about 2 x10 23 protons and an equal number of electrons. If the penny is charged to +1C, what fraction of the electrons have been added or removed? fraction removed =.00003 !

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Check Question: If you remove one electron from a quarter and one electron from a Buick, which (if either) has the greater net charge?

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Conductivity conductors: loosely bound electrons; charge flows freely insulators: tightly bound electrons; charge hard to move

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Induction in a conductor EBONITE How will the +’ve charge move? How will the -’ve charge move?

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Induction in a conductor EBONITE I see a problem; do you see a problem?

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Induction in a conductor EBONITE

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Induction in a conductor EBONITE Where is the +’ve charge? Where is the -’ve charge?

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Induction in an insulator EBONITE

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Induction in an insulator EBONITE

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Induction in an insulator EBONITE Look at the surface. F net

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Induction conductors: charge flows insulators: charge shifts

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Newton’s Law of Gravity M1M1 M2M2 r Constant of proportionality

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M earth = 5.98 x 10 24 kg r = 6.38 x 10 6 m What is the force between the Earth and a book? W earth,book = M book (9.8 N/kg) W earth,book = (6.67 x 10 -11 Nm 2 ) (5.98 x 10 24 kg) M book (6.38 x 10 6 m) 2 kg 2

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Gravitational Field consider a 1kg block F = ?10 N F = ?5 N

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Gravitational Field consider a 3kg block F = ?10 N F = ?3 kg x 5 N/kg = 15 N gravitational field strength What is the gravitational field strength at the Earth’s surface?

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Gravitational Field What is the gravitational field strength at this point? m = 5 kg F = 35 N 7 N/kg

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Gravitational Field 10 N/kg 7 N/kg 5 N/kg F = m g

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Electric Force Definition: Coulomb’s Law Electric field is the force that +1C would feel if it were placed at this location.

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What units? Newtons (N) Coulombs (C) q is in units of: k : 9 x 10 9 N.m 2 /C 2 F is in units of: E is in units of: N/C

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Example #1 Anthea rubs two latex balloons against her hair, causing the balloons to become charged negatively with 2.0 x 10 -6 C. She holds them a distance of 0.70 m apart. A) what is the electrical force between the two balloons? B) Is it one of attraction or repulsion?

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Example 2 Anthea rubs two latex balloons against her hair, causing the balloons to become charged negatively with 2.0 x 10-6 C. She holds them a distance of 0.70 m apart. A) what is the electrical force between the two balloons? B) Is it one of attraction or repulsion? C) What is the electrical field of the 1 st balloon?

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Example #3 At the location marked with an x, the electric field is 2000 N/C and points right. What is the electric force (size and direction) on a 6 x 10 -6 C charge that is placed at the x? EF F = qE = (6x10 -6 )(2000) = 1.2 x 10 -2 N (to the right) +q+q 20 3 3 60

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Example #3 cont. What if the charge were the same size but negative? EF Same size F = 60 N (to the left) F = Who Knows? -q-q What if a charge were placed somewhere else? E

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Electric Fields (again)

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Electric Field Operational definition: Electric field is the force that +1C would feel if it were placed at this location.

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Example #2 A charge of -5 x 10 -8 C feels a force of 0.2 N to the right. What is the electric field (magnitude and direction) at the charge’s location? FE F = qE -q-q E = F/q E = 4 x 10 6 N/C (to the left)

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Where does E come from? Force on q due to the field, E, at q’s location Field at q’s location due to other charges at other locations (source charges) The charge that is feeling the force (test charge)

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What is the direction of the electric field at x? E The direction of E E What is the direction of the electric field at x? HOW BIG?

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Coulomb’s Law E r k = 9 x 10 9 Nm 2 /C 2 qsqs E = k q s r2r2

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Example #last A 2.5 x 10 -6 C charge is placed as shown below. What is the electric field at a point 5 cm to the right? qsqs 5 cm E = kq s /r 2 = (9 x 10 9 )(2.5 x 10 -6 ) /(5 x 10 -2 ) 2 = +9 x 10 6 N/C Which way does E point?

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Coulomb’s Law E r k = 9 x 10 9 Nm 2 /C 2 qsqs E = k q s r2r2

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Q1Q1 Q2Q2 What is the electric field strength at the location of Q 1 due to Q 2 ? Which charge do we care about? 0.20 m -6 x 10 -9 C3 x 10 -9 C

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Q2Q2 0.20 m What is the electric field strength at the location of Q 1 due to Q 2 ? Which charge do we care about? How does this change the problem? -6 x 10 -9 C

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Q2Q2 E = kq s /r 2 = (9 x 10 9 )(6 x 10 -9 ) /(0.20) 2 = 1350 N/C 1350 N/C -6 x 10 -9 C

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Q2Q2 1350 N/C What force does Q 1 experience? F = qE = (3 x 10 -9 C)(1350 N/C) = 4 x 10 -6 N (right) 4 x 10 -6 N

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Q1Q1 Q2Q2 0.20 m What is the electric field strength at the location of Q 2 due to Q 1 ? Which charge do we care about? 3 x 10 -9 C-6 x 10 -9 C

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0.20 m What is the electric field strength at the location of Q 2 due to Q 1 ? Which charge do we care about? How does this change the problem? Q1Q1 3 x 10 -9 C

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E = kq s /r 2 = (9 x 10 9 )(3 x 10 -9 ) /(0.20) 2 = 675 N/C 675 N/C Q1Q1 3 x 10 -9 C

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Q1Q1 What force does Q 2 experience? 4 x 10 -6 N F = qE = (6 x 10 -9 C)(675 N/C) = 4 x 10 -6 N (left) 675 N/C

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4 x 10 -6 N 675 N/C1350 N/C 4 x 10 -6 N due to Q 1 due to Q 2 F 2,1 F 1,2

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Q1Q1 Q2Q2 0.20 m What is the electric field at the midpoint between the charges? Which charge do we care about?

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Q1Q1 Q2Q2 What is the electric field at the midpoint between the charges? E 2,X E 1,X

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Q1Q1 Q2Q2 What is the electric field at the midpoint between the charges? E net E X,2 E X,1 = kq s /r 2 = (9 x 10 9 )(3 x 10 -9 ) /(0.10) 2 = 2700 N/C E X,2 = kq s /r 2 = (9 x 10 9 )(6 x 10 -9 ) /(0.10) 2 = 5400 N/C E net = 8100 N/C

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Q1Q1 Q2Q2 What force would a charge Q 3 = -2 x 10 -6 C experience if placed at the midpoint? E net = 8100 N/C F = qE = (2 x 10 -6 C) (8100 N/C) = 0.016 N F

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4 x 10 -6 N F 2,1 F 1,2 Q1Q1 Q2Q2

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Two point charges +Q and -Q are fixed in place a distance 2d apart as shown. What direction is the electric field at the midpoint between the charges? +Q-Q Student 2: “The electric field is given by E=kq s /r 2 so if I do the calculation I get: E net = k(+Q)/d 2 + k(-Q)/d 2 = 0 So, the electric field is zero and has no direction.” dd What do you think?

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Two identical positive charges, A and B, are arranged as shown. The distance from point C to A is twice the distance from point C to B. Which of the following best represents the electric field at point C? e d c b a A BC

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e d c b a A BC

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Distributed Charge: or what if charge were peanut butter? +Q +Q/9

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Distributed Charge: or what if charge were peanut butter? +Q +Q/9

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Distributed Charge: or what if charge were peanut butter? +Q +Q/9

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Distributed Charge: or what if charge were peanut butter? +Q +Q/9

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Distributed Charge: or what if charge were peanut butter? +Q +Q/9

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Distributed Charge: or what if charge were peanut butter? +Q +Q/9

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Distributed Charge: or what if charge were peanut butter? +Q +Q/9

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Distributed Charge: or what if charge were peanut butter? +Q +Q/9

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Distributed Charge: or what if charge were peanut butter? +Q +Q/9

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Distributed Charge: or what if charge were peanut butter? +Q +Q/9

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Distributed Charge: or what if charge were peanut butter? +Q +Q/9 What if all the charge were moved to the bottom?

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Distributed Charge: or what if charge were peanut butter? +Q +Q/9

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Distributed Charge: or what if charge were peanut butter? +Q +Q/9

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What is the electric field in the middle of the circle?

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Boston Museum of Science

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From Tutorial

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L = - 0 /2 L = + 0 /2 R = - 0 /2 R = + 0 /2

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L = - 0 /2 L = + 0 /2 R = - 0 /2 R = + 0 /2 E = 0

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L = - 0 /2 L = + 0 /2 R = - 0 /2 R = + 0 /2

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L = - 0 /2 L = + 0 /2 R = - 0 /2 R = + 0 /2 E 0

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L = + 0 R = - 0 E-E- E+E+

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L = + 0 R = - 0 E = 0

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L = + 0 R = - 0 E-E- E+E+

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L = + 0 R = - 0 E = 0

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L = + 0 R = - 0 E-E- E+E+ = 0 /2 0

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L = + 0 R = - 0 E = 0 / 0

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Charles Allison © 2000 Chapter 21, Electric Charge, and electric Field.

Charles Allison © 2000 Chapter 21, Electric Charge, and electric Field.

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