(Knight Chapter 31, Problem 63) What are the current passing through
the battery Ibat and the potential difference Vab between points a
and b when the switch in the figure below is (a) open, and (b) closed?
31.63.
Model:
The battery and the connecting wir
A positive charge +q is located at (0, d) in the xy plane.
a) How much work is needed to bring a second charge +3q from
infinity to the point P (0, +d)? (Assume potential energy
between two charges separated by infinity to be zero)
b) What is the electr
VECTOR CALCULUS SUMMARY
LINE INTEGRAL: The notation
F dl means that at every point on
C
the curve C, evaluate the value of F dl and add up all values
from all the points on loop C by integration. The vector dl ,
(as described in lecture notes Chapter 1, P
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3». Is. mittr
3_i. .24 a} if Gr: .5:
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mA :d EMA 4 Jildlf' = 3!
5 A= 41"?
A I it
6 = Can(4+?o')i+53"(?")?
n. 35 urn0
A. 1  B A *
ar9= z+? i
Example: Vector and coordinate systems
j
Given the vector A 3i 2 k , express it in terms of cylindrical coordinates defined by the vector
A , i.e. express A a r r a a z z . You have to determine the unit vectors r , , z , expressing them in
j,
terms of
Detailed Information on the Final Examination of PHYS1415
A. About the final examination:
(1) The final examination will make up 50% of your total marks, and is an important component of
the course.
(2) The final examination will cover from Chapter 1 (Vec
Practice questions for PHYS1415 Midterm test (1 hour)
1. [15 points] Consider an electric dipole of two charges +q and q
separated at a distance d.
(a) Determine the dipoles electric potential energy. [3]
(b) A second electric dipole is introduced so tha
Updated on 12 Feb 2012
PHYS 1415 3:006:00 pm
Feb
Mon Tue Wed Thur
wk 25 13
Venue: Rm 104. Chong Yuet Ming physics building
Laboratory 1: Operation of a Cathode Ray Oscilloscope (CRO)
Group 1
Group 2
Fri Days
Laboratory 2: The A. C. Circuitry
Group 1
Grou
PHYS1415 General Physics II Midterm Test Suggested Solution
1.
(a) Define the concentric cubic Gaussian surface as S, using Gauss law, the
electric flux is related to the enclosed charge by
E =
(b) No. The term
Q
E
PHYS 1415 General Physics II Spring 2012 Homework # 7 Solutions
1. (a) Express the magnetic field strength at P using the expression for B due to a
straight wire segment:
I
BP 0 sin 1 sin 2
4 R
where
a
sin 1 sin 2
R a2
2
Substitute for sin1 and sin2 to
PHYSICS 1415
GENERAL PHYSICS II
HOMEWORK 7
DUE DATE: April 30, 2012
All assignments must be returned to the Chong Yuet Ming Physics Building 1/F
assignment boxes before 2:00pm. NO LATE HOMEWORK WILL BE ACCEPTED.
1. [15] Tipler & Mosca (6th edition) chapte
PHYS1415 General Physics II
Assignment 6 Solution (Spring 2012)
1. According to the problem, we can approximately use the infinite solenoid formula:
B 0 nI
a). I1 2.0 A, I 2 0 A
b). I1 2.0 A, I 2 1.5 A
c). I1 2.0 A, I 2 1.5 A
d) (i)Since the diamagnetic
PHYSICS 1415
GENERAL PHYSICS II
HOMEWORK 6
DUE DATE: April 16, 2012
All assignments must be returned to the Chong Yuet Ming Physics Building 1/F
assignment boxes before 2:00pm.
NO LATE HOMEWORK WILL BE ACCEPTED.
1. [15] A solenoid 50cm long with 1200 turn
PHYS1415 General Physics II
Assignment 5 Solution (Spring 2012)
1.(a) The current density of this cylinder is
I
r r22
To apply Ampere's law, we can treat the system as a round cylinder with no hole
through it, plus a second cylinder with the same current
PHYSICS 1415
HOMEWORK 5
GENERAL PHYSICS II
DUE DATE: April 2, 2012
All assignments must be returned to the Chong Yuet Ming Physics Building 1/F
assignment boxes before 2:00pm.
NO LATE HOMEWORK WILL BE ACCEPTED.
1. [15] A long, round copper cylinder 12 cm
PHYS1415 General Physics II Spring 2012 Assignment #4 Solutions
1. Because the bar is a uniform conductor,
EL = V = 1.5 V
Then the electric field strength us E =1.5/2=0.75 V/m along the bar.
And hence the current density
The total current flowing through
PHYSICS 1415
HOMEWORK 4
GENERAL PHYSICS II
DUE DATE: March 19, 2012
All assignments must be returned to the Chong Yuet Ming Physics Building
1/F assignment boxes before March 19, 2012 (Monday) 2:00pm.
NO LATE HOMEWORK WILL BE ACCEPTED.
1. [15] A copper ba
Homework assignment 4
Problem 1
1
0
If A
0
0
0
1
0
0
2 3
1 0
0 1
14
, B
1 0
6 3
0 1
0 2
0
0
1
2
0
0
, find AB.
2
0
[Hint: dividing the matrix into blocks may simplify the calculation]
Problem 2
A, B, C are all n by n square matrices, and we have AB BC
PHYS1415 General Physics II
HOMEWORK 3 Solution (Spring 2012)
1. Utilizing Gauss' Law in the neighborhood of each surface with the knowledge that
electric field equals zero within metal in equilibrium, the equations below are attained.
Charge conservation
HW3
Problem 1
Use the Green theorem to evaluate the following line integral:
x
2
y 2 dx 4 x 2 dy
C
where C is a closed loop of the perimeter
R ( x , y )  x 2, 0 y 2 in an anticlockwise sense.
of
the
rectangular
region
Solution:
x y dx 4 x dy 8 x 2 x y
HW3
Problem 1
Use the Green theorem to evaluate the following line integral:
x
2
y 2 dx 4 x 2 dy
C
where C is a closed loop of the perimeter
R ( x , y )  x 2, 0 y 2 in an anticlockwise sense.
of
the
rectangular
region
Problem 2
Use the divergence theor
PHYSICS 1415 GENERAL PHYSICS II
HOMEWORK 3
DUE DATE: March 2, 2012
All assignments must be returned to the Chong Yuet Ming Physics Building
1/F assignment boxes before 2:00pm on 2012 March 2 (Friday).
NO LATE HOMEWORK WILL BE ACCEPTED.
1. [10] Knight (2nd
PHYS1415 General Physics II HOMEWORK 2 Solution (2012 Spring)
1. (a) In cylindrical coordinates,
dl drr rd dzz
r=A, dr=0, dz=0,
For the loop C,
(i)
For F (r 3 ) / 2r 2 ,
(ii)
For F k sin( / 3) ,
(b) For the semicircular loop C,
(i) For F (r 3 ) / 2r 2 ,
PHYS1316 Assignment 2:Line, Surface, and Volume integrals
Problem 1
The work done of a particle under a force field F along a path C is given by
F dr.
C
Find the work done in moving a particle in the force field
F 3x 2 i 2 xz y j zk
along the space curve
PHYS1316 Assignment 2
Problem 1
The work done of a particle under a force field F along a path C is given by
F dr.
C
Find the work done in moving a particle in the force field
F 3x 2 i 2 xz y j zk
along the space curve C ( x , y , z)  x 2t 2 , y t , z 4
PHYS1415 General Physics II HOMEWORK 1 Solution (2012 Spring)
1.
(a) From
  
,
 
(
)
()
(
 
(
)
()
()
)
)
Then we get
(
) (
  
so
(
)
(b)
Since
 
, so
Since
 
, so
(C)


Then the unit vector of


is
(d)
Cylindrical coordinates:
?
Problem 1
Find the gradients of the following functions:
(a) ( x, y , z ) x 2 y 2 z 2
(b) ( x, y , z ) exp( x y ) cos z
Solution 1
(a)
2
2
2
grad i
x j y k z ( x y z )
i
( x 2 y 2 z 2 ) j
(x2 y2 z2 ) k (x2 y2 z2 )
x
y
z
2 xi 2 yj 2 zk
(b)
grad i
x j y