Physics 202, Lecture 2 · Physics 202, Lecture 2 Todayʼs Topics Electric Force and Electric Fields...
Transcript of Physics 202, Lecture 2 · Physics 202, Lecture 2 Todayʼs Topics Electric Force and Electric Fields...
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!
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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 ∞)
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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