# What is Electricity? zFlow of electrons. zElectromagnetic force.

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What is Electricity? zFlow of electrons. zElectromagnetic force

BASIC MODEL

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”

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

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?

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

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 #

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

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

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 !

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

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

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

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

Induction in a conductor EBONITE

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

Induction in an insulator EBONITE

Induction in an insulator EBONITE

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

Induction conductors: charge flows insulators: charge shifts

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

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

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

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?

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

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

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

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

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?

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?

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

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

Electric Fields (again)

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

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)

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)

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?

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

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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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?

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

e d c b a A BC

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Boston Museum of Science

From Tutorial

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

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

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

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

 L = +  0  R = -  0 E-E- E+E+

 L = +  0  R = -  0 E = 0

 L = +  0  R = -  0 E-E- E+E+

 L = +  0  R = -  0 E = 0

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

 L = +  0  R = -  0 E =  0 /  0

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