Transcript An old rule of thumb

Ch3 Quiz 1
Last name
___________________
First name______________________
Section number______
There is an electric field given by


E  E0ix
where E0 is a constant.
What is the difference in the value of the electric potential
due to this electric field between the origin and the point
x=a, y=b?
Ch3 Quiz 3
There is an electric field created by some source at the
origin given by 
c 
E  4 ir
r
where
c
is
a
constant
and
r
is
the
distance
from
the
origin;

ir points out from the origin.
What is the difference in the value of the electric potential
due to this electric field between the point x=a, y=b and
the point at infinity?
What is the potential function corresponding to this
electric field if instead of being at the origin the source
of the electric field is at point x=a, y=b?
Ch3 Quiz 2
Last name
___________________
First name______________________
Section number______
There is an electric field given by



2
2
E   x ix  y i y
where  and  are constants.
What is the difference in the value of the electric potential
due to this electric field between the origin and the point
x=a, y=b?
In electrostatics, the electric field is conservative:
 
E

d
r

0

In electrostatics:
U
U
Fx  
Fy  
x
y
V
V
Ex  
Ey  
x
y
If we know V(x,y) we can find the components of electric field E x and E y
1)The electric potential V in a region of space is given by
V ( x, y)  A( x  3 y )
2
2
where A is a constant. Derive an expression for the
electric field at any point in this region.
2)The electric potential V in a region of space is given by
c
V (r ) 
3r 3
where c is a constant. The source of the field is at the
origin. Derive an expression for the electric field at any
point in this region.
Exercise 5 p. 52
An electron moves from one point to another where the
second point has a larger value of the electric potential by
5 volts. If the initial velocity was zero, how fast will the
electron be going at the second point?
Electric potential V is a scalar!
An
old
rule
ofofthumb:
you
have
totostudy
2-3
hours
aaweek
An
old
rule
thumb:
you
have
study
2-3
hours
week
An
old
rule
of
thumb:
you
have
to
study
2-3
hours
a
week
outside
the
class
per
each
credit
hour
An
old
rule
of
thumb:
you
have
to
study
2-3
hours
a
week
outside
the
class
per
each
credit
hour
An
old
rule
of
thumb:
you
have
to
study
2-3
hours
a
week
outside
the
class
per
each
credit
hour
An
old
rule
of
thumb:
you
have
to
study
2-3
hours
a
week
outside
the
class
per
each
credit
hour
An
old
rule
of
thumb:
you
have
to
study
2-3
hours
a
week
outside
the
class
per
each
credit
hour
An
old
rule
of
thumb:
you
have
to
study
2-3
hours
a
week
outside
the
class
per
each
credit
hour
An
old
rule
of
thumb:
you
have
to
study
2-3
hours
a
week
outside
the
class
per
each
credit
hour
An
old
rule
of
thumb:
you
have
to
study
2-3
hours
a
wee
outside
therule
class
per each
credit
hour
An
old
of
thumb:
you
have
to
study
2-3
hours
a
we
outside
the
class
per
each
credit
hour
An
old
rule
of
thumb:
you
have
to
study
2-3
hours
a
w
outside
the
class
per
each
credit
hour
An
old
rule
of
thumb:
you
have
to
study
2-3
hours
a
outside
the
class
per
each
credit
hour
outside
the
class
per
each
credit
outside the class per each credithour
hour
Electric field lines
These are fictitious lines we sketch which point in
the direction of the electric field.

1) The direction of E at any point is tangent to the
line of force at that point.
2) The density of lines of force in any region is
proportional to the magnitude of E in that region
Lines never cross.
Density is the number of lines going through an area (N)
divided by the size of the area
At R1
R1 R
2
At R2
N
density 
2
4R1
N
density 
2
4R2
N
At any r density 
4r 2
1
q
For a charge q located at the origin E 
40 r 2
density  E
It is important that the force is proportional to 1
r2
Gauss’s Law
The total flux of electric field out of any
closed surface is equal to the charge
contained inside the surface divided by  0 .
  Qenclosed
 E  dS 
S
0
 
E  dS
What is
water flow?
or flux of any vector, e.g. velocity of a

Consider a flow with a velocity vector v .
Let S be a small area perpendicular to v .
v
v
S
a)
b)

S  Sn
S

n
Area
 vector
Flux:
 
  vS cos  v  S
a) The volume of water flowing through S per unit time is
vS

b) Now S is tilted with respect to v . The volume of water flowing
through S per unit time is vS cos


 is the angle between velocity vector v and unit vector n
normal to the surface S.

Flux of electric field E
S
S
Hw quiz
Suppose Coulomb’s Law for the force between charges
and q2 was

q1q2
F   4 rˆ
r
with  some constant. Find the potential function
corresponding to such a force and the electric potential
function.
q1
Have a great day!
Please don’t
pictures
forget
your
Hw: All Chapter 3 problems
and exercises
Reading: Chapter 3