AP Physics III.A

Electrostatics

18.1 Origin of Electricity

The Fundamental Charge (Robert Millikan and his oil drop

experiment)

Ex. How many electrons are in two Coulombs of negative charge?

18.2 Charged Objects and Electric Force

Law of Conservation of Charge – during any one process, net

electrical charge of an isolated system remains constant.

Ex. Two identical isolated conducting spheres, one with charge -6 μC and another with net charge +2 μC are allowed to touch. If the two spheres have the same net charge after touching, what is the net charge on each sphere?

Attractions and repulsions

18.3 Conductors and Insulators

18.4 Charging by Induction and Conduction (also known as, “I

wish I had a decent electroscope”)

Charging by Conduction

Charging by Induction

Induced charge on an insulator

18.5 (Charles De) Coulomb’s Law

“Hmm, this looks like something I’ve seen before”

Ex. An electron “orbits” the proton of a hydrogen atom at an average distance of 0.53 EE 10-10 m. What is the force that theproton exerts on the electron? What is the velocity of the electronfor a circular orbit?

Ex. Two charges exert electrical force F on each other. If the magnitude of each charge is doubled and the distance between them is halved, what is the force F′ on each charge in terms of F?

Electric forces and vectors

Ex. Three Charges in a Line

Ex. Three Charges in a Plane

p. 552: 3-5, 7, 11, 15, 19, 21, 23, 79B7

4. 3.4 EE -17 kg, mA > mB

79B7

a) FBD

b) k

mglq

tansin2

18.6 Electric Field

A mass in a gravitational field

Charges experience an electrostatic force due to the presence of other

charges

Force per Coulomb is the definition of an electric field

(“show me the formula”)

An electric field is a vector that has a direction that the force exerts

on a positive test charge.

Some examples

Ex. Find the electric force on a proton placed in an electric fieldof 2.0 EE 4 N/C that is directed along the positive x-axis.

Electric fields are vectors. The net electric field at a point in space can be determined by

considering the contributions of each charged object and adding

them together as vectors.

Electric field produced by a point charge

Ex. Electric Field Between Two Point Charges. Two point chargesare separated by a distance of 0.100 m. One has a charge of –25.0μC and the other 50.0 μC . a) What is the magnitude and directionof the electric field at point P between them 0.020 m from the negative charge? b) If an electron is placed at rest at P, what isthe magnitude and direction of its initial acceleration?

Symmetry and the electric field.

18.7 Electric Field Lines

Field lines around positive and negative charges

Field lines between plates of a capacitor.

Field lines between two dipoles

Field lines between two identical charges

p. 553: 25, 29, 31, 35-37; 81B3

36. a) 182 N/C b) 312 N/C

81B3

a) FBD

b) E = 5800 N/C, FT = 0.058 N

c) drawing

19.1 Electric Potential Energy

Work done on a charge in a uniform electric field

Let’s clarify but not overemphasize the signs

19.2 Electric Potential Difference

Let’s look at “gravitational potential” first

OK, now electric potential

So change in electric potential is . . .

Electric potential decreases or increases not because the field exerts

any more or less force (the field is uniform – like gravity near the

Earth’s surface). V changes because of distance. A charge released in the

field, traveling a greater distance converts more of its Ue to K (like dropping an object from a greater

height).

Everyday examples

Potential (and therefore potential difference) is scalar (this will

simplify some things).

Summary

• Electric potential energy – energy a charge has because of its potential in an electric field (so far the field is uniform)

• Electric potential – electric potential energy per unit charge

• Potential difference – change in electric potential

Another formula and an hilarious story about twin boll weevils.

Muy importante – the displacement of the charge is in

the direction of the electric field.

Ex. In the figure shown, the work done on a 2.0 µ C charge by the electric field from A to B is 5.0 EE -5 J. What is the change in electric potential energy and the potential difference?

A · B ·

Worth noting: a positive charge accelerates from a higher potential to lower potential. A negative charge accelerates from lower potential to

higher potentials.

Conservation of Energy – yep, here it is again with electrical potential energy in the picture

Ex. A proton is released in a uniform electric field with a magnitude of 8.0 EE 4 V/m directed along the positive x-axis. The proton undergoes a displacement of 0.50 m in the direction of the field. a) Find the potential difference. b) Find the change in electrical potential energy c) Find the speed if the proton starts from rest.

The electron-volt – the change in electrical potential energy as an

electron moves through a potential difference of one volt

Ex. A particle with mass of 1.8 EE -5 kg and a charge of 3.0 EE -5 C is released from rest at point A and accelerates horizontally to point B. The only force on the particle is the force from the electric field and the electric potential at A is 25 V greater than the potential at B. What is the velocity of the particle at B?

p. 581: 4, 6; p. 150: 36

4. a) 2.00 EE -14 J b) 2.00 EE -14 J

6. a) 1500 V b) B is higher potential

36. 2700 m

19.2 Electric Potential Due to a Point Charge

Graphically – potential from a positive charge is positive and decreases to zero at infinity.

Potential from a negative charge is negative and increases towards zero

at infinity.

Electric Potential for a Pair of Point Charges

Ex. A 5.0 µC charge is at the origin and a -2.0 µC charge is on the x-axis at (3.0, 0) m. a) If the electric potential is zero at infinity, find the total electric potential due to the charges at P, with coordinates (0, 4.0) m. b) How much work is required to bring a third charge of 4.0 µC from infinity to P?

Ex. How many places are there on the line below where the potential is zero? Where is (are) these locations?

2q -q

Ex. Potential energy for a group of charges

p. 582: 11-17; 87B2, 89B2

12. 2.4 (let VA = VB)

14. 45 V

16. 0.37 m (let U2 = 2U1)

87B2

a) 9 EE 4 V

b) 9 EE -2 V

c) 0.30 N

d) 8.0 EE 5 N/C (right)

e) 6 m/s (use con. of mom. and con. of E)

89B2

a) -2 microC

b) 3.6 N (right)

c) -0.72 J

d) 0.16 m e) ?