Charge is invisibly small but sparks are visible! What are they made of? Why can we see them?

The sudden cascade of many electrons leaping across the gap produce the visible flash of light Light is NOT made up of electrons. When electrons jump they create “electromagnetic waves”of light.

m proton = kg m electron = kg m proton = 1 e  q e =  10  19 Coulomb 1836  m electron Despite the mass difference, they carry exactly equal, but opposite, electric charges. q e electric charge on 1 electron q P electric charge on 1 proton = 

How many electrons are there in 1 Coulomb of negative charge? How many protons are there in 1 Coulomb of positive charge? 1 e  q e =  10  19 Coulomb 6,241,800,000,000,000,000 protons

Two uniformly charged spheres are firmly fastened by insulated stands to frictionless pucks which are set on an air table Which force diagram below correctly shows the magnitude and direction of the electrostatic forces? The charge on sphere 2 is 3  the charge on sphere 1.

F electro- static  Q1·Q2 Q1·Q2 F  1R21R2 electro- static Charles Coulomb (1736 – 1806) F = k Q1·Q2R2Q1·Q2R2 electro- static

F = k Q1·Q2R2Q1·Q2R2 electro- static k =  10 9 N·m 2 C 2 which we can compare to: F = G m1·m2R2m1·m2R2 grav G = 6.67  10  11 N·m 2 kg 2

What force exists between two concentrations of charge, each 1 coulomb separated by a center- to-center distance of 1 meter? (1 C)(1 C) (1 m 2 ) = 2,020,390,000 lbs = 1,010,195 tons  lb/N =  10 9 N

 0.8 grams each W  N BALLOON’S WEIGHT STRING’S TENSION ELECTROSTATIC REPULSION T F W q  1 or 2  10  7 Coulomb The charge holding our balloons apart:

4 discrete charges of magnitude, q, and the indicated (+/  ) signs, occupy the corners of a rectangle as shown. The direction of the electric field, E, at the point shown is: 1) up 2) left 3) right 4) down 5) other +q qq qq

4 discrete charges of magnitude, q, and the indicated (+/  ) signs, occupy the corners of a rectangle as shown. The direction of the electric field, E, at the point shown is: 1) up 2) left 3) right 4) down 5) other +q qq qq

4 discrete charges of magnitude, q, and the indicated (+/  ) signs, occupy the corners of a rectangle as shown. The direction of the electric field, E, at the point shown is: 1) up 2) left 3) right 4) down 5) other +q qq qq

 +

+2 q -3q-3q

Similarly, the earth can be thought of as surrounded by a gravitational field, or g-field. Locally, near its surface, the g-field is constant and points down everywhere. Its constant value ( g = 9.8 m/sec 2 ) is represented by the uniform spacing between field lines. Note: the weight of any object is determined by multiplying its mass by the local value of g.

Further away from earth’s surface the g-field weakens. This decrease with distance is seen in the spreading out of field lines!

Recall = M object g mass  acceleration Similarly: For a localized concentration of charge,Q Q R q = q E The electric field [Force per coulomb of charge] describes the effective strength of a charge in terms of its potential influence on any other charge that enters the space surrounding it.

A spherical conductor carries a charge uniformly distributed across its surface: 1.(A)out of the page. 2.(B)into the page. 3.(C)left into sphere. 4.(D)diagonally: left/up. 5.(E)points into page. 6.(F) diagonally : right/up. 7.(G)points away. 8.(H) diagonally : right/down. 9.(I)points down. 10.(J) diagonally : left/down. E CG I D F HJ The E-field at the indicated position, points:

The electric field at the very CENTER of this spherical conductor E = ? 1. points out4. points left 2. points in5. points right 3. points up6. points down 7. is zero

What is the electric field at the very CENTER of this spherical conductor? E = 0!!

E = ? 1. points out4. points left 2. points in5. points right 3. points up6. points down 7. is zero The electric field at this off-CENTER point within the spherical conductor

The electric field at this off-CENTER point within the spherical conductor will be countered exactly by the that due to the equal amount of charge just as far away below. The electric field due to charge directly above this position In fact a ring of equally distant charge will all have their influence at this point cancelled!

The electric field at this off-CENTER point within the spherical conductor Nearby charges create a strong electric field. Much farther away, individual charges have a much smaller effect, but there are much more of them! All of this balances beautifully and the electric field even at off-center points (in fact, EVERYWHERE ) within the conductor is zero!

That’s why fan motors or transformers (which can produce fluctuating electric fields) are often shielded from the more sensitive parts of circuits by “cans” of conducting metal.

Conducting panels when screwed in place provide a surrounding shield against stray electric fields!

5) other QUESTION 2 At the very center the electric field due to any single charge is exactly opposite to the field created by the charge at the opposite corner! 1) up QUESTION Net electric field is up. 2) left QUESTION Net electric field is left QUESTION 1 G. points away. QUESTION 5 For a spherical collection of charge the field lines are all directed along radial lines (for positive charge pointing straight out from the center).