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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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Course Details

We will not go over the course details in class, you can find them at

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

Or go directly to

http://web.mit.edu/8.02t/www/miscellaneous/8.02%20Introduction_v02.pdf

Are their any burning questions about course details?

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W01D2: Outline

Introductions

Course Overview

Vector and Scalar Fields

Charge

Electric Force

Electric Field

Introductions

Announcements

Math Review Tuesday Tues Feb 14 from 9-11 pm in 32-082

PS 1 due Tuesday Tues Feb 14 at 9 pm in boxes outside 32-082 or 26-152

W01D3 Reading Assignment Course Notes: Chapter 1.1-1.7, 2.1-2.7

Bring Clickers to Monday/Tuesday Class

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8.02: Electricity and MagnetismAlso 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

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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 temperatureContour 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

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Electric ForceThe 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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Coulomb's Law

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

unit vector from q1 to q2

vector from q1 to q2

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Coulomb's Law: Example

a = 1 m

q1 = 6 C

q3 = 3 C

q2 = 3 C

32r

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The Superposition Principle

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.

NOTE: Solutions will be posted within two days of class

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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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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 :

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

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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:

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Concept Question Answer: 5 Equal Charges

E fields of the side pairs cancel (symmetry) E at center due only to top charge (R away) Field points downward

Alternatively:

“Added negative charge” at bottom R away, pulls field down

Answer 4.

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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 LinesElectric 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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Concept Question Answer: Field Lines

NOTE: This is different than flow lines (3). Particles do NOT move along field lines. (1) is not correct because we don’t know sign of charge so we don’t know direction of force

Answer: 2. Directions positive charges accelerate.

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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:

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Summary

Charge qs (±)

CREATE:

FEEL:

SOURCE:

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Concept Question: Electric FieldTwo 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.

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Concept Question Answer: Electric Field

Answer: 3. To the left of the positively charged object on the left

Between: field points from positively charged object to negatively charged object

On right: field is dominated by negatively charged object

On left: electric field due to close smaller positively charged object will cancel electric field due to further larger negatively charged object.

http://web.mit.edu/viz/EM/visualizations/electrostatics/ElectricFieldConfigurations/pcharges/pcharges.htm