Physics 014 Physics 014 Lecture 1Lecture 1

Chapter 21 Electric ChargeChapter 21 Electric Charge

Office hours: Thirkield Hall, Room 215, MWF 12:00-1:00pm (or by appointment)

Phone: (202) 806-6257

Email: mengshw@gmail.com

My Research: Atmospheric PhysicsNumerical Modeling

Dr. Mengs H. Weldegaber

Course DetailsCourse Details• See: Syllabus, schedule, grade policy, …

• Text: Fundamentals of Physics, Halliday, Resnick, and Walker, 9th edition. We will cover chapters 21-36 in this class.

• Exams: Midterm: 11 Oct 2013Final Exam (cumulative): 13 Dec 2013

• Quizzes: Weekly.

• Grades: Homework 30%, Quizzes 15% , Midterm Exam 20% Final Exam 35%.

What are we going to learn?What are we going to learn?A road mapA road map

• Electric charge Electric force on other electric charges Electric field, and electric potential

• Moving electric charges : current • Electronic circuit components: batteries, resistors, capacitors• Electric currents Magnetic field

Magnetic force on moving charges• Time-varying magnetic field Electric Field• More circuit components: inductors, AC circuits. • Maxwell’s equations Electromagnetic waves light waves• Geometrical Optics (light rays). • Physical optics (light waves): interference, diffraction.

Let’s get started!Let’s get started!Electric chargesElectric charges

• Two types of charges: positive/negative• Like charges repel• Opposite charges attract

Atomic structureAtomic structure : • negative electron cloud• nucleus of positive protons, uncharged neutrons

Electric Charge

(a) Two charged rods of the same sign repel each other.

(b) Two charged rods of opposite signs attract each other. Plus signs indicate a positive net charge, and minus signs indicate a negative net charge.

12F1q 21F 2q

12F 1q 21F2qor

12F1q 21F2qor

Force between pairs of point Force between pairs of point charges: Coulomb’s lawcharges: Coulomb’s law

Coulomb’s law -- the force between point charges:

• Lies along the line connecting the charges.

• Is proportional to the magnitude of each charge.

• Is inversely proportional to the distance squared.

• Note that Newton’s third law says |F12| = |F21|!!

Charles-Augustin de Coulomb (1736-1806)

2q12F1q 21F

12r

Coulomb’s lawCoulomb’s law

212

2112

||||||

rqqk

F

2

212

00

1085.8with 41

mN

Ck

2

291099.8

CmNk =

For charges in aVACUUM

Often, we write k as:

Materials classified based on their ability to move charge

• Conductors are materials in which a significant number of electrons are free to move. Examples include metals.

• The charged particles in nonconductors (insulators) are not free to move. Examples include rubber, plastic, glass.

• Semiconductors are materials that are intermediate between conductors and insulators; examples include silicon and germanium in computer chips.

• Superconductors are materials that are perfect conductors, allowing charge to move without any hindrance.

Electric charges in solidsElectric charges in solids• In macroscopic solids, nuclei

often arrange themselves into a stiff regular pattern called a “lattice”.

• Electrons move around this lattice. Depending on how they move the solid can be classified by its “electrical properties” as an insulator or a conductor.

• In a conductor, electrons move around freely, forming a “sea” of electrons. This is why metals conduct electricity.

• Charges can be “induced” (moved around) in conductors.

Charges in solidsCharges in solids

Blue background = mobile electrons

Red circles = static positive charge (nuclei)

-

-

+

+

Insulating solidsInsulating solids

• In an insulator, each electron cloud is tightly bound to the protons in a nucleus. Wood, glass, rubber.

• Note that the electrons are not free to move throughout the lattice, but the electron cloud can “distort” locally.

+ -

How to charge an objectHow to charge an object• An object can be given some “excess” charge: giving

electrons to it (we give it negative charge) or taking electrons away (we “give” it positive charge).

• How do we do charge an object? Usually, moving charges from one surface to another by adhesion (helped by friction), or by contact with other charged objects.

• If a conductor, the whole electron sea redistributes itself.

• If an insulator, the electrons stay where they are put.

Conservation of ChargeConservation of Charge

You connect these together with a metal wire; what is the final charge distribution?

? ?

Total amount of charge in an isolated system is fixed (“conserved”)

+1C 2C

Example: 2 identical metal spheres have charges

+1C and –2C.

Conservation of Electric Charges

• A glass rod is rubbed with silk

• Electrons are transferred from the glass to the silk

• Each electron adds a negative charge to the silk

• An equal positive charge is left on the rod

Conservation of Electric Charges

• A very hard rubber rod is rubbed with animal fur

• Electrons are transferred from the fur to the rubber

• Each electron adds a negative charge to the rubber

• An equal positive charge is left on the fur

(very hard rubber)

Quantization of ChargeQuantization of Charge

• Charge is always found in INTEGER multiples of the charge on an electron/proton ([[why?]])

• Unit of charge: Coulomb (C) in SI units• Electron charge = –e = 1.6 x 10-19 Coulombs• Proton charge = +e = +1.6 x 10-19 Coulombs• One cannot ISOLATE FRACTIONAL CHARGE

(e.g. 0.8 x 10-19 C, +1.9 x 10-19 C, etc.) [[but what about quarks…?]]

• Unit of current: Ampere = Coulomb/second

SuperpositionSuperposition

• Question: How do we figure out the force on a point charge due to many other point charges?

• Answer: consider one pair at a time, calculate the force (a vector!) in each case using Coulomb’s Law and finally add all the vectors! (“superposition”)

• Useful to look out for SYMMETRY to simplify calculations!

Multiple Forces: If multiple electrostatic forces act on a particle, the net force is the vector sum (not scalar sum) of the individual forces.

Shell Theories: There are two shell theories for electrostatic force

Answer: (a) left towards the electron (b) left away from the other proton (c) left

2q12F1q 21F

12r

Coulomb’s law, Coulomb’s law, ReviewReview

212

2112

||||||

rqqk

F

2

291099.8

CmNk =

F12 kq1 q2

r2

8.99 109 N m2 C2 3.0 10 6C 4.0 10 6C 0.20m 2 2.7N

F13 kq1 q3

r2 8.99 109 N m2 C2 3.0 10 6C 7.0 10 6C

0.15m 2 8.4N

5.7NN4.8N7.21312 FFF

Example 1. Find the net force on q1 ?

Soln

Example 2. Find the net force on q3 ?

• The force exerted by q1 on q3 is

• The force exerted by q2 on q3 is

• The resultant force exerted on q3 is the vector sum of and

13F

23F

13F

23F

F kq1 q2

r2

8.99 109 N m2 C2 1.60 10 19C 2

5.29 10 11m 2 8.22 10 8N

rmvmaF c2

v Fr m 8.22 10 8N 5.29 10 11m

9.1110-31kg2.18 106 m s

Example 3. Determine the speed of the electron in orbit about the nuclear proton at a radius of 5.29x10-11 m, assuming the orbit to be circular [The Bohr model of the hydrogen atom]?

Soln

Example 4: Example 4: Find the force onFind the force on qq11

• Three equal charges form an equilateral triangle of side 1.5 m as shown

• Compute the force on q1

• What is the force on the other charges?

d

q1

d

dq2

q3

q1= q2= q3= 20 C

Solution: Set up a coordinate system, compute vector sum of F12 and F13

d

1

2

3

d

d

12F

13F

o60y

x

SummarySummary• Electric charges come with two signs: positive and negative.

• Like charges repel, opposite charges attract, with a magnitude calculated from Coulomb’s law: F=kq1q2/r2

• Atoms have a positive nucleus and a negative “cloud”.

• Electron clouds can combine and flow freely in conductors; are stuck to the nucleus in insulators.

•We can charge objects by transferring charge, or by induction.

• Electrical charge is conserved, and quantized.