Example: 4-momentum, c=1 convention, and neutrino beams
!
The 4-momentum of a particle of rest mass m velocity ! is given by
" $ E "'
"
"
!
p = m ! " ( c, # ) = & , p )
with E = " mc 2 and p = " m#
%c (
(1.1)
where ! = 1 / 1 " # 2 and ! = " / c . With the
Whasmg H1, HW M W W
we w w m yaw W. ac
ox 565% as; W5. \5 carwm they:
- 1
* g; S E AV
k\\
gvab,
an we MA +3 m M Mvmsnw Rt m Rug
lwsiée améx cerrside 11». Sew. Oxsuck «u. 69%.
RC, Coxwbv» 06:
ENS: 9;? gar (Wm Wok "'5
ox MSKl+ weve alNaiar M Wm] "F
Name_
Ph-142 Homework Set 3
(Version 1.0)
Due Wednesday, Jan 27, 2010
In general, it is OK to work with others in understanding how to do homework
problems but all work that you turn in must be entirely your own.
There are several example problems from Pu
Name_
Ph-142 Homework Set 2
(Version 1.0)
Due Wednesday, Jan 20, 2010
In general, it is OK to work with others in understanding how to do homework
problems but all work that you turn in must be entirely your own.
There are several example problems from Pu
Name_
Ph-142 Homework Set 1
Due Wednesday, Jan 13, 2010
(Version 1.0)
In general, it is OK to work with others in understanding how to do homework
problems but all work that you turn in must be entirely your own.
First, close your book and notes and deriv
Example Purcell 3-9
Solution (Part A):
Consider the 4 charges in the sketch above. Note that the figure is symmetrical under the
combined operations a) x ! " x and b) +Q ! "Q . Because of this charge-mirror-symmetry
about the x-axis, its clear that the x-
Example Purcell 2-26
Solution:
If the square has a side S, then the inscribed circle would have to have
a smaller potential at the center, and the superscribed circle would have to
have a larger potential. I would think a very good estimate would be that
Example 8-12
Solution:
First note that the two parallel paths, A and B, have exactly the same impedance since
they contain the same elements in series. The current in each path is the same, and is
equal to the applied voltage divided by this impedance:
IA
Example Purcell 1.12
Solution:
Let a be the length of one side of the triangle. Choose the origin of coordinates to
be the center of the base and choose the y-axis to be the perpendicular bisector of the
base. base. With this geometry, the positions of th
Example 3: Surface and volume integrals.
a)
Find the surface area of a rectangle of sides A and B:
The differential area is dx ! dy , and the limits of integration are uncorrelated, so the
total area is
A
B
0
0
A = " d! = " dx dy = " dx " dy = AB
V
b)
V
(
Ph142 (Winter 2010)
Jan 7, 2010
Example 2: Gausss Law
Find the electric field due to a uniformly charged sphere of radius R and
constant charge density !0 for a
Solution: Use Gausss Law. First note that the electric field must have
spherical symmetry (sam
Ph142 (Winter 2010)
Jan 7, 2010
Example 1(a) : Suppose a regular hexagon is inscribed in a circle of radius R. If a charge
Q is placed at each vertex of the hexagon, find the magnitude and direction of
the electric field at the center of the circle.
Solut