SET 5
2.22)
We did this problem in class. Evaluate the integral;
dx
V = 2
0
= 2 ln(x +
[x + y 2 ]1/2
2
x2 + y 2 ) |
0
The issue here is understanding how to remove the , which after all is a constant. If
integration is taken between then one needs to cons
SET 4
2.7)
dE
r
z
R
Figure 1: The coordinate geometry for the problem
From the gure R + r = z and
r 2 = |z R|2 = R2 + z 2 2R z cos()
Also;
z R cos()
cos() = z r r =
|z R |
We need only the z component of the electric eld. Thus;
z R cos()
]
|z R |3
1 (R/z
SET 3
1.49)
For 3 vectors
F1 = x2 z
F2 = x2 x + y y + z z
F3 = yz x + zxy + xy z
Then;
F1 = 0
F2 = 3
F1 = x3 /3
y
F2 = V ;
where V = 1/2(x2 + y 2 + z 2 )
F3 = 0
F3 = V ; where
V = (xyz )
F3 = 0
F3 = curlA ; where A = (1/2)[x(z 2 y 2) + y (x2 z 2 ) +
SET 2
1.30)
z
(0,0,1)
y
(0,1,0)
(1,0,0)
x
Figure 1: The coordinate geometry for the problem
The integration is over the surfaces in the (x,y), (y,x), (x,z), and the triangular area
shown in the gure. The integral is then;
1
V=
dz z 2
0
(1z y )
(1z )
dx
dy
SET 1
1.6)
Write the cross product B C in cartesian coordinates;
BC =
xy
z
Bx By Bz
Cx Cy Cz
B C = x[By Cz Bz Cy ] + y [Bx Cz Bz Cx ] + z [Bx Cy By Cz ]
Then take the cross product A (B C ). This is rearranged and terms collected to
obtain;
A (B C ) = B (
Phys 6321 Midterm - Solution
March 18, 2013
You must do all problems in the time allocated. You may NOT use any notes or
books other than those provided by the instructor do you own work. You may
NOT receive aid from anyone other that the instructor. Show
Phys 6321 Final Exam - Solutions
May 3, 2013
You may NOT use any book or notes other than that supplied with this test. You
will have 3 hours to nish. DO YOUR OWN WORK. Express your answers clearly and
concisely so that appropriate credit can be assigned
Phys 4321 Exam 1 Solutions
Sept. 19, 2013
1)
A line charge of constant linear density, is in the shape of a circular arc of radius, a,
centered on the origin. It lies in the (x, y ) plane beginning at the positive x axis and ending
at the negative x axis,