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Physics 8.02T http://web.mit.edu/8.02t/www

For now, please sit anywhere, 9 to a table

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8.02 Course Notes Revised

Introduction to Electricity and Magnetism

Dourmashkin, Belcher, and Liao

Online at

http://web.mit.edu/8.02t/www/coursedocs/current/guide.htm

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W01D2: Outline

Introductions Course Overview Vector and Scalar Fields Charge Electric Force Electric Field

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Course Details

We will not go over all the course details in class, you can click the link 8.02 Introduction

on http://web.mit.edu/8.02t/www/

Or go directly to

http://web.mit.edu/8.02t/www/materials/Presentations/8.02_Introduction.pdf

Online Registration If you are in a M/W/F class for 8.02, you will need to register for the course “8.02r-MW Electricity and Magnetism (Monday and Wednesday)”. If you are in a Tuesday/Thursday/Friday class for 8.02, register for “8.02r-TTh: Electricity and Magnetism (Tuesday and Thursday)”. The following link will get you to either course and the web site will require certificates: https://lms.mitx.mit.edu/

Reading Questions Answer Reading Questions online in the appropriate course for your section. Reading Questions due at 8:30 am the day of class. The following link will get you to either course and the web site will require certificates: https://lms.mitx.mit.edu/

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Problem Sets For each week’s problem set: 1)  you will submit your answers to two problems

online in the appropriate course for your section.

2)  You will hand in your answers to six written problems in your section slot in the boxes outside the door of 32-082 or 26-152 depending on which is your classroom. Make sure you clearly write your name and section on your problem set.

3)  Both online and handwritten are due Tues 9 pm

Announcements

Math Review Week Two Tuesday from 9-11 pm in 26-152 PS 1 due Week Two Tuesday at 9 pm. Submit two problems on online and hand in six problems in the appropriate section boxes outside 32-082 or 26-152 Bring Clickers to Monday/Tuesday Class

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8.02: Electricity and Magnetism Also new way of thinking… How do objects interact at a distance?

Fields We will learn about electric & magnetic fields: how they are created & what they affect

Maxwell’s Equations

Lorentz Force Law

E ⋅dA

S∫∫ =

Qin

ε0

E ⋅d s

C∫ = − d

dtB ⋅dA

S∫∫

B ⋅dA

S∫∫ = 0

B ⋅d s

C∫ = µ0Ienc + µ0ε0

ddt

E ⋅dA

S∫∫

F = q(

E+ v ×

B)

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Scalar and Vector Fields

Review Vector Analysis

in

Online Course Notes http://web.mit.edu/8.02t/www/coursedocs/current/guide.htm

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Scalar Fields

Temperature Scalar Field: every location has an associated value (number with units)

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Scalar Fields - Contours

Colors represent surface temperature Contour lines show constant temperatures

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Vector Fields Vector (magnitude, direction) at every

point in space

Example: Velocity vector field - jet stream

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Coulomb’s Law, Electric Fields and

Discrete Charge Distributions

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Electric Charge

Two types of electric charge: positive and negative Unit of charge is the coulomb [C]

Charge of electron (negative) or proton (positive) is

Charge is quantized

Charge is conserved

±e, e = 1.602×10−19C

Q = ±Ne

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Electric Force The electric force between charges q1 and q2 is (a)  repulsive if charges have same signs (b)  attractive if charges have opposite signs

Like charges repel and opposites attract !!

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Charging

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How Do You Get Charged?

•  Friction •  Transfer (touching) •  Induction

+q Neutral - - - -

+ + + +

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Demonstrations: Instruments for Charging

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Demonstration: Bouncing Balloon

Van de Graaf Generator D17

Why is the balloon attracted to the metal sphere?

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Coulomb's Law Coulomb’s Law: Force on q2 due to interaction between q1 and q2

ke =

14πε0

= 8.9875×109 N m2 /C2

F12 = ke

q1q2

r122 r12

r12 : unit vector from q1 to q2

r12 =

r12r12

⇒F12 = ke

q1q2

r123

r12

r12 : vector from q1 to q2

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In Class Problem: Coulomb's Law Vector Analysis

Find a vector expression for the unit vectors in terms of

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r32 =?

r12 =?

r31 =?

i and j.

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Coulomb's Law: Example

r32 = ( 12 i − 3

2 j) mr32 = 1m

a = 1 m

q1 = 6 C

q3 = 3 C

q2 = 3 C

F32 = ?

F32 = keq3q2

r32

r323

r32

= (81×109 )

2( i − 3j) N

= (9×109 N ⋅m2 C2 )(3C)(3C)

12 ( i − 3j)m

(1m)3

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The Superposition Principle

F3 =F13 +

F23

Fj =

Fij

i=1

N

∑

Many Charges Present: Net force on any charge is vector sum of forces from other individual charges

Example:

In general:

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In Class Problem: Force on a Charged Object

Three charged objects are located at the positions shown in the figure. Find a vector expression for the force on the negatively charged object located at the point P.

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Electric Field

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Electric Field The electric field at a point P due to a charged object (source) with charge qs is the force acting on a test point-like charged object with charge qt at that point P, divided by the charge qt :

Es(P) ≡

Fst (P)

qt

Es(P) = ke

qs

rst2 rs(P)

Units: N/C

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Superposition Principle

The electric field due to a collection of N point charges is the vector sum of the individual electric fields due to each charge

E =E1 +E2 + . . . . .=

Ei

i=1

N

∑

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Concept Question: 5 Equal Charges

Six equal positive charges q sit at the vertices of a regular hexagon with sides of length R. We remove the bottom charge. The electric field at the center of the hexagon (point P) is:

1.E = 2kq

R2 j 2.E = − 2kq

R2 j 5.E = 0

4.E = − kq

R2 j 3.E = kq

R2 j

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Group Problem: Electric Field on Axis (Symmetry)

d

s

q− q+

P

Consider two point charges of equal magnitude but opposite signs, separated by a distance d. Point P lies along the perpendicular bisector of the line joining the charges, a distance s above that line. What is the E field at P?

ij

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Electric Field Lines 1.  Direction of field at any point is tangent to field

line at that point 2.  Field lines point away from positive charges

and terminate on negative charges 3.  Field lines never cross each other

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Concept Question: Field Lines Electric field lines show:

1.  Directions of forces that exist in space at all times.

2.  Directions in which positive charges on those lines will accelerate.

3.  Paths that charges will follow. 4.  More than one of the above. 5.  I don’t know.

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Force on a Charge Object in an Electric Field

Force on a charged object with charge q at a point P in an electric field due to a source is:

Fq (P) = q

Es(P)

Es

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Concept Question: Electric Field Two charged objects are placed on a line as shown below. The magnitude of the negative charge on the right is greater than the magnitude of the positive charge on the left, . Other than at infinity, where is the electric field zero?

1.  Between the two charged objects. 2.  To the right of the charged object on the right. 3.  To the left of the charged object on the left. 4.  The electric field is nowhere zero. 5.  Not enough info – need to know which is positive.

qR > qL

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Summary

Charge qs (±)

Es = ke

qs

rst2 rst

FE = q

E

CREATE:

FEEL:

SOURCE: