Download Dipoles, Flux and Gauss`s Law (6/18)

Chapter 21
{
© 2012 Pearson Education, Inc.
Electric Fields and Dipoles (cont.)
Q21.7
Two point charges and a point P lie
at the vertices of an equilateral
triangle as shown. Both point
charges have the same negative
charge (–q). There is nothing at
point P.
The net electric field that charges
#1 and #2 produce at point P is in
Charge #1
–q
P
y
–q
x
A. the +x-direction.
B. the –x-direction.
C. the +y-direction.
D. the –y-direction.
E. none of the above
© 2012 Pearson Education, Inc.
Charge #2
A21.7
Two point charges and a point P lie
at the vertices of an equilateral
triangle as shown. Both point
charges have the same negative
charge (–q). There is nothing at
point P.
The net electric field that charges
#1 and #2 produce at point P is in
Charge #1
–q
P
y
–q
x
A. the +x-direction.
B. the –x-direction.
C. the +y-direction.
D. the –y-direction.
E. none of the above
© 2012 Pearson Education, Inc.
Charge #2
Q21.9
Positive charge is uniformly
distributed around a semicircle.
The electric field that this
charge produces at the center
of curvature P is in
A. the +x-direction.
B. the –x-direction.
C. the +y-direction.
D. the –y-direction.
E. none of the above
© 2012 Pearson Education, Inc.
A21.9
Positive charge is uniformly
distributed around a semicircle.
The electric field that this
charge produces at the center
of curvature P is in
A. the +x-direction.
B. the –x-direction.
C. the +y-direction.
D. the –y-direction.
E. none of the above
© 2012 Pearson Education, Inc.
Q21.10
Three point charges lie at the
vertices of an equilateral triangle
as shown. Charges #2 and #3
make up an electric dipole.
The net electric torque that
charge #1 exerts on the dipole is
A. clockwise.
Charge #2
+q
Charge #1
+q
y
x
B. counterclockwise.
C. zero.
D. not enough information given to decide
© 2012 Pearson Education, Inc.
–q
Charge #3
A21.10
Three point charges lie at the
vertices of an equilateral triangle
as shown. Charges #2 and #3
make up an electric dipole.
The net electric torque that
charge #1 exerts on the dipole is
A. clockwise.
Charge #2
+q
Charge #1
+q
y
x
B. counterclockwise.
C. zero.
D. not enough information given to decide
© 2012 Pearson Education, Inc.
–q
Charge #3
Q21.11
Charge #2
+q
Three point charges lie at the
vertices of an equilateral triangle
as shown. Charges #2 and #3
make up an electric dipole.
The net electric force that charge
#1 exerts on the dipole is in
Charge #1
+q
y
–q
x
A. the +x-direction.
B. the –x-direction.
C. the +y-direction.
D. the –y-direction.
E. none of the above
© 2012 Pearson Education, Inc.
Charge #3
A21.11
Charge #2
+q
Three point charges lie at the
vertices of an equilateral triangle
as shown. Charges #2 and #3
make up an electric dipole.
The net electric force that charge
#1 exerts on the dipole is in
Charge #1
+q
y
–q
x
A. the +x-direction.
B. the –x-direction.
C. the +y-direction.
D. the –y-direction.
E. none of the above
© 2012 Pearson Education, Inc.
Charge #3
Chapter 22
{
© 2012 Pearson Education, Inc.
Gauss’s Law
Gauss’s Law
•
•
Gauss’s law is an alternative to Coulomb’s law and is
completely equivalent to it.
Carl Friedrich Gauss, shown below, formulated this law.
© 2012 Pearson Education, Inc.
Charge and electric flux

Positive charge within the box produces outward electric flux through the
surface of the box, and negative charge produces inward flux. (See Figure
22.2 below.)
© 2012 Pearson Education, Inc.
Zero net charge inside a box

Figure below shows three cases in which there is zero
net charge inside a box and no net electric flux through
the surface of the box.
© 2012 Pearson Education, Inc.
What affects the flux through a box?

As Figure below shows, doubling the charge within the box doubles the
flux, but doubling the size of the box does not change the flux.
© 2012 Pearson Education, Inc.
Calculating electric flux

Electric Flux Through a Rectangular Surface
© 2012 Pearson Education, Inc.
Electric flux through a disk
© 2012 Pearson Education, Inc.
Electric flux through a cube
•
Evaluate total Electric Flux through cube.
© 2012 Pearson Education, Inc.
Electric flux through a sphere
•
Calculate total Flux due to point charge.
© 2012 Pearson Education, Inc.
Point charge centered in a spherical surface
•
The flux through the
sphere is independent of
the size of the sphere and
depends only on the
charge inside. Figure at
the right illustrates this
fact.
© 2012 Pearson Education, Inc.
Point charge inside a nonspherical surface
•
As before, the flux is independent of the surface and depends
only on the charge inside. (See Figure 22.12 below.)
© 2012 Pearson Education, Inc.
Positive and negative flux
•
Figure 22.14 below shows that flux is positive if
the enclosed charge is positive, and negative if
the charge is negative.
© 2012 Pearson Education, Inc.
Q22.1
A spherical Gaussian surface (#1)
encloses and is centered on a point charge
+q. A second spherical Gaussian surface
(#2) of the same size also encloses the
charge but is not centered on it.
Compared to the electric flux
through surface #1, the
flux through surface #2 is
A. greater.
B. the same.
Gaussian
surface #1
C. less, but not zero.
D. zero.
E. not enough information given to decide
© 2012 Pearson Education, Inc.
+q
Gaussian
surface #2
A22.1
A spherical Gaussian surface (#1)
encloses and is centered on a point charge
+q. A second spherical Gaussian surface
(#2) of the same size also encloses the
charge but is not centered on it.
Compared to the electric flux
through surface #1, the
flux through surface #2 is
A. greater.
B. the same.
Gaussian
surface #1
C. less, but not zero.
D. zero.
E. not enough information given to decide
© 2012 Pearson Education, Inc.
+q
Gaussian
surface #2
Using Gauss’s law
•
What is the total Flux through the surfaces
A,B,C, and D shown below? iClickers…
© 2012 Pearson Education, Inc.
Q22.2
Two point charges, +q (in
red) and –q (in blue), are
arranged as shown.
Through which closed
surface(s) is the net
electric flux equal to zero?
A. Only surface A
B. Only surface B
C. Only surface C
D. Only surface D
E. Both surface C and surface D
© 2012 Pearson Education, Inc.
A22.2
Two point charges, +q (in
red) and –q (in blue), are
arranged as shown.
Through which closed
surface(s) is the net
electric flux equal to zero?
A. Only surface A
B. Only surface B
C. Only surface C
D. Only surface D
E. Both surface C and surface D
© 2012 Pearson Education, Inc.