PS1 - Electricity and Magnetism Physics 2217 and AEP 2170...

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Unformatted text preview: Electricity and Magnetism Physics 2217 and AEP 2170 Spring 2011 Homework 1 Assigned: Monday January 24th Due: Friday January 28rd 1. Problem 1.1 Purcell 2. Problem 1.2 Purcell 3. Problem 1.3 Purcell The next few problems are meant to give you an idea of the math that will be required this semester. We will discuss gradients, divergences, and curls over the next couple of weeks, but we will focus on the beautiful physics that these mathematical objects describe rather than answer “how do I calculate x.” (I just want to give you an idea of what’s ahead.) 4. Let

 
 a. Calculate
the
gradient
 b. Integrate
the
gradient
of
T
along
the
following
three
paths
 i. (0,0,0)
→
(1,0,0)
→
(1,1,0)
→
(1,1,1)

 T · dl ii. (0,0,0)
→
(0,0,1)
→
(0,1,1)
→
(1,1,1)

 P 2;y=x
 iii. the
parabolic
path
z=x 
 5. Let


 
 a. Calculate
the
divergence
 b. Integrate
the
divergence
of
v
over
the
volume
of
a
cube
with
sides
=2.
(the
 four
corners
are:
000,
200,
020,
002).

 
 
 
 
 
 
 c. Integrate
v
over
each
surface
of
the
cubic.

 d. What
is
the
result
of
integrating
over
the
entire
surface?
 
 
 
 e. Calculate
the
curl
of
v.
 f. Integrate
the
curl
of
v
over
5
of
the
6
sides
of
the
cube
(don’t
integrate
over
 the
side
in
the
yz
plane
intersecting
the
origin)
 
 
 g. Integrate
v
over
the
boundary
(0,0,0)
→
(0,1,0)
→
(0,1,1)
→
(0,0,1)
→
(0,0,0)

 ...
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This note was uploaded on 06/10/2011 for the course PHYS 2217 taught by Professor Leclair, a during the Spring '06 term at Cornell University (Engineering School).

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