physics 202, lecture 2physics 202, lecture 2 ... 1 2 12 21 r q q f = k e. numeric examples: electric...
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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
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.
For deep thinkers: Why electrons and protons have the same electric charge?
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: permitivity of free space
+ - + - + + - -
221
2112 rqq
kFF e==
Numeric Examples: Electric Force Is Strong
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 large:
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 Note: Multiple particles on charge i, Fi= F1i+F2i+ F3i +….
1221221
21
12221
12
ˆ
ˆ
FrrqqKF
rrqqKF
e
e
−==
=E. Force on q2 by q1:
E. Force on q1 by q2: 12r̂
r
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
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. (chapter 23)
Properties of the Electric Force
rqqkU e 21=
)()(2121if
i
e
f
er
rUU
rqqk
rqqkrdFW f
i
−−−=+−=•= ∫
Note the similarities and differences to gravity
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 Field view of electric force:
q1 creates an electric field E around it The electric field E applies a force on q2
12221
12 r̂rqqKF e=
221221
2 ˆ qEqrrqKF e
==
E
In this field view: q1: source charge q2: test charge E independent of q2
12
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)
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 ∞)
16
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
17
Exercise: An Electron in a Uniform E. Field
Find out vertical displacement after the electron pass through a downward uniform electric field E
For an electron charge e and mass m Answer: dy = - ½at2 = = - ½(F/m) (t)2 =- ½(eE/m) (l/vi)2