Gauss' Law = Coulomb's Law
Daniel Jensen
Purdue University
September 12, 2011
Daniel Jensen
(Purdue)
Gauss' Law
September 12, 2011
1 / 11
Outline
1
Introduction
2
Gauss' Law
Daniel Jensen
(Purdue)
Gauss' Law
September 12, 2011
2 / 11
Administrative Stu
Personal Purdue website: http://web.ics.purdue.edu/∼jensend/
Homework hints 4 and 5 posted
CHIP
Homework 4 due Wednesday night
Homework 5 due Friday night
Grades
Misspellings
Email comments
danielsjensen1@gmail.com or jensend@purdue.edu
Include the words Physics 241 in email
Show example email
Class members only
Attendance policy
Daniel Jensen
(Purdue)
Gauss' Law
September 12, 2011
3 / 11
Gauss' Law
Denition and description
Qenc
ε0
‹
= Φtot =
~E · n̂ dS
Gauss' Law = Coulomb's Law
No I'm not lying, Gauss' Law = Coulomb's Law
Daniel Jensen
(Purdue)
Gauss' Law
September 12, 2011
4 / 11
Quiz Question 1
A point charge is placed at the center of a spherical Gaussian surface. The
electric ux ΦE is changed if:
A) the sphere is replaced by a cube of the same volume
B) the sphere is replaced by a cube of one-tenth the volume
C) the point charge is moved o center (but still inside the original
sphere)
D) the point charge is moved to just outside the sphere
E) a second point charge is placed just outside the sphere
Daniel Jensen
(Purdue)
Gauss' Law
September 12, 2011
5 / 11
Quiz Question 1
Exam 1 Fall 2002 - Problem 6
A point charge is placed at the center of a spherical Gaussian surface. The
electric ux ΦE is changed if:
A) the sphere is replaced by a cube of the same volume
B) the sphere is replaced by a cube of one-tenth the volume
C) the point charge is moved o center (but still inside the original
sphere)
D) the point charge is moved to just outside the sphere X
E) a second point charge is placed just outside the sphere
Daniel Jensen
(Purdue)
Gauss' Law
September 12, 2011
5 / 11
Quiz Question 2
Consider a spherical Gaussian surface of radius 1 m, which surrounds two
electric dipoles and two charges (one positive and one negative) as shown
in the gure. Here q1 = 7 nC, q2 = −4 nC, and p1 = p2 = 10−10 C·m.
What is the net electric ux through
the Gaussian surface? Use
2
−
12
2
ε0 = 8.85 × 10
C / N·m .
A) 339 N·m2 /C
B) 7059 N·m2 /C
C) 2325 N·m2 /C
D) 561 N·m2 /C
E) 4649 N·m2 /C
Daniel Jensen
(Purdue)
Gauss' Law
September 12, 2011
6 / 11
Quiz Question 2
Exam 1 Fall 2003 - Problem 4
Consider a spherical Gaussian surface of radius 1 m, which surrounds two
electric dipoles and two charges (one positive and one negative) as shown
in the gure. Here q1 = 7 nC, q2 = −4 nC, and p1 = p2 = 10−10 C·m.
What is the net electric ux through
the Gaussian surface? Use
2
−
12
2
ε0 = 8.85 × 10
C / N·m .
A) 339 N·m2 /C X
B) 7059 N·m2 /C
C) 2325 N·m2 /C
D) 561 N·m2 /C
E) 4649 N·m2 /C
Daniel Jensen
(Purdue)
Gauss' Law
September 12, 2011
6 / 11
Quiz Question 3
An isolated conductor of arbitrary shape has a net charge
−6 C. Inside the conductor there is a cavity within which is
Qnet = 35.5 × 10
a point charge q = 10.9 × 10−6 C. What is the charge qwall on the cavity
wall and the charge qout on the outer surface of the conductor?
= 0 × 10−6 C,
A)
qwall
B)
qwall
C)
qwall
D)
qwall
= −46.4 × 10−6 C,
E)
qwall
qout
qout
= −10.9 × 10−6 C,
= −10.9 × 10−6 C,
= 0 × 10−6 C,
Daniel Jensen
(Purdue)
= −35.5 × 10−6 C
qout
qout
qout
= 46.4 × 10−6 C
= 35.5 × 10−6 C
= 46.4 × 10−6 C
= 35.5 × 10−6 C
Gauss' Law
September 12, 2011
7 / 11
Quiz Question 3
Exam 1 Fall 2003 - Problem 3
An isolated conductor of arbitrary shape has a net charge
−6 C. Inside the conductor there is a cavity within which is
Qnet = 35.5 × 10
a point charge q = 10.9 × 10−6 C. What is the charge qwall on the cavity
wall and the charge qout on the outer surface of the conductor?
= 0 × 10−6 C,
A)
qwall
B)
qwall
C)
qwall
D)
qwall
= −46.4 × 10−6 C,
E)
qwall
qout
qout
= −10.9 × 10−6 C,
= −10.9 × 10−6 C,
= 0 × 10−6 C,
Daniel Jensen
(Purdue)
= −35.5 × 10−6 C
qout
qout
qout
= 46.4 × 10−6 C X
= 35.5 × 10−6 C
= 46.4 × 10−6 C
= 35.5 × 10−6 C
Gauss' Law
September 12, 2011
7 / 11
Quiz Question 4
Charge is distributed uniformly on the surface of a spherical balloon (an
insulator) with a point charge q inside. The electrical force on q is greatest
when:
A) it is near the inside surface of the balloon
B) it is at the center of the balloon
C) it is halfway between the balloon center and the inside surface
D) it is anywhere inside (the force is the same everywhere and it is not
zero)
E) it is anywhere inside (the force is zero everywhere)
Daniel Jensen
(Purdue)
Gauss' Law
September 12, 2011
8 / 11
Quiz Question 4
Exam 1 Fall 2002 - Problem 2
Charge is distributed uniformly on the surface of a spherical balloon (an
insulator) with a point charge q inside. The electrical force on q is greatest
when:
A) it is near the inside surface of the balloon
B) it is at the center of the balloon
C) it is halfway between the balloon center and the inside surface
D) it is anywhere inside (the force is the same everywhere and it is not
zero)
E) it is anywhere inside (the force is zero everywhere) X
Daniel Jensen
(Purdue)
Gauss' Law
September 12, 2011
8 / 11
Practice Question
An innite line of charge produces a eld E = 4 × 10−6 N/C at a point P
that is a distance 2 m from the line. Calculate the linear charge density λ .
A) 0.89 × 10−3 C/m
B) 4.45 × 10−4 C/m
C) 8.94 C/m
D) 1.7 × 10−3 C/m
E) 8 C/m
Daniel Jensen
(Purdue)
Gauss' Law
September 12, 2011
9 / 11
Practice Question
Exam 1 Fall 2002 - Problem 2
An innite line of charge produces a eld E = 4 × 10−6 N/C at a point P
that is a distance 2 m from the line. Calculate the linear charge density λ .
A) 0.89 × 10−3 C/m
B) 4.45 × 10−4 C/m X
C) 8.94 C/m
D) 1.7 × 10−3 C/m
E) 8 C/m
Daniel Jensen
(Purdue)
Gauss' Law
September 12, 2011
9 / 11
Summary
Gauss' Law
Daniel Jensen
(Purdue)
Gauss' Law
September 12, 2011
10 / 11
For Further Reading I
A. Author.
Handbook of Everything
Some Press, 1990.
S. Someone.
On this and that.
.
. 2(1):50100, 2000.
Journal on This and That
Daniel Jensen
(Purdue)
Gauss' Law
September 12, 2011
11 / 11