Physics 202, Lecture 2 · Physics 202, Lecture 2 Todayʼs Topics Electric Force and Electric Fields Electric Charges and Electric Forces Coulomb's Law Physical Field The Electric

Physics 202, Lecture 2 Today’s Topics

  Electric Force and Electric Fields   Electric Charges and Electric Forces   Coulomb's Law   Physical Field   The Electric Field   Electric Field Lines

  Motion of Charged Particle in Electric Field

  Expected from preview: electric force, Coulomb’s law, electric field, field lines,….

A Reminder

Lectures supplement but do not substitute for reading !

Lecture Effectiveness = Preview + Lectures + Review

Review: Properties of Electric Charges   2+1 types: positive, negative (+neutral).   Unit: Coulomb (C). 1 C= charge of 6.24x1018 protons.   Electric charge is quantized: q=±Ne, e=1.602x10-19 C   Building blocks of matters:

  Electric charge is conserved: charges can be moved

around, but the total charge remains the same.

Charge (C) Mass (kg) Electron -e=-1.602x10-19 9.11x10-31

Proton +e=+1.602x10-19 1.673x10-27

Neutron 0 1.675x10-27

Electric Force And Coulomb’s Law  Electric forces exist between two charged particles  The direction of electric force depends on the signs of the

charges:   forces between opposite sign charges are attractive   forces between like sign charges are repulsive

 The magnitude of the electric forces for point charges

(Coulomb’s Law) Coulomb Constant: ke = 8.987x109Nm2/C2 = 1/(4πε0) ε0=8.854x10-12C2/(Nm2): permittivity of free space

+ - + - + + - -

221

2112 rqq

kFF e==

Numeric Examples: Electric Force Is Huge

  Electric force between two 1C charges 1 meter apart: F=8.99x109N

 Proton and electron in a hydrogen atom: qelectron= -1.6x10-19 C, qproton= 1.6x10-19 C, r=5.3x10-11m à Electric force F= 8.2 x10-8 N.   This force is huge:

  Compared to the mass of proton: 1.673x10-27 kg   Compared to the gravitational forces between them:

FG= 3.6x10-47N (recall: FG=Gm1m2/r2)

  Four fundamental forces: Strong > Electromagnetic > Weak >> Gravitational

Coulomb’s Law in Vector Form

  Exercise: Use this vector form to verify the attractive/repulsive feature

!F12 = Ke

q1q2r2

r12

!F21 = Ke

q1q2r2

r21 = !!F12

E. Force on q2 by q1:

E. Force on q1 by q2: 12r

r

 Multiple particles on charge i, Fi= F1i+F2i+ F3i +….

Quick Quiz   Two charges, q1=0.1C and q2=5q1 (i.e.0.5C), are separated by a

distance r=1m. Let F2 denotes the force on q2 (exerted by q1), and F1 denotes the force on q1 (exerted by q2). Which of the following relationship is true?   F1=5F2   F1=-5F2   F2=-5F1   F1=-F2

Math Reminder: Vectors   Vector: a math quantity with a magnitude and a direction.

  Visually: An arrow with a length and a direction.   Unit vector : a vector with length=1

  Vector sum and subtraction. (review yourself)

  Vector de-composition (projection):

  Forms of Coulomb’s Law:

!r = r ! r

!r

!r = a x + b y = a i + b j

r

a

b

i

j

!F12 = Ke

q1q2r2

r12 = Keq1q2r3"r12

Exercise: Electric Forces Due to Two Charged Particles

  Find the electric force on q3. Solution: See board.

  It is one of four fundamental forces: Strong >Electromagnetic > weak >> gravity   It is proportional to 1/r2 : double r à ¼ F

  Its direction is charge sign dependent: like signà repulsive, opposite sign à attractive   It is a conservative force. (Work independent of path)  A potential energy can be defined. (Ch. 25)

Properties of the Electric Force

rqqkU e 21=

)()(2121if

i

e

f

er

rUU

rqqk

rqqkrdFW f

i

−−−=+−=•= ∫

A Very Important Concept: Field

 What is a physical “field” ?

Field: A physical quantity which has a physical value* at each point in space (i.e. a distribution).

Examples of physical fields: temperature, wind speed, electric field, magnetic field, …   In this course, we consider only scalar and vector forms of

physical quantities.

Example of Scalar and Vector Fields

Wind speed (vector) Temperature (scalar)

Measurement can be made at any point on the map.

The Coulomb’s Law Revisited   Original (Coulomb’s) view of electric force:

q1 directly applies an electric force on q2  “Modern” view of electric force:

  q1 creates an electric field E around it   The electric field E applies a force on q2

12221

12 rrqqKF e=

221221

2 ˆ qEqrrqKF e

==

E

In this modern view: q1: source charge q2: test charge E independent of q2!

14

Electric Field and Electric Force

q0

q r

rrqKe ˆ20=E

qrrqKq e EF ˆ20==

q0: source charge E: field by q0 q: test charge F = qE force on q by E

Visualization of Electric Field: Field Lines   Use of field lines is a convenient way to visualize electric fields   Simple rules for drawing field lines:

  line direction: direction of E vector   line density: relative strength of E. (denser = larger)

Field Lines e.g.: Point-Like Charges

+q -q

Magnitude E=ke q/r2 Magnitude E=ke q/r2

Example 2: Two Charged Particles

+q and +q +q and - q (dipole)

Each field line always starts from a + q and end at a -q (or ∞)

18

Motion Of Charged Particle In The Electric Field

  Fundamental Formulas:   F=qE

  a=F/m = qE/m   v= vi +at

E

+q

-q

If initially rest (vi =0) then v= at = (qE/m) t

Motion of +q: Same dir. as E

Motion of - q:

Opposite dir. as E

19

Exercise: An Electron in a Uniform E. Field

 Find out vertical displacement after the electron pass through a downward uniform electric field E

 Solution: Exercise with your TAs Answer: dy= - ½ (e/m)E (l/vi)2