Problem 1: Consider a long wire along the y-axis with a current of 12 A in the
negative y-direction. What is the force per length on this wire if it sits in a magnetic
eld of 2.5 104 T in the positive z-direction? Give the answer as a vector.
In this case
CALCULUS II (PHSCI/ENG) 110.109 HOMEWORK WEEK 03
(1) Evaluate the integral
R
tan5 x sec3 x dx
R sin
d
cos3
R
(3) Evaluate the integral csc4 x cot6 x dx
(2) Evaluate the integral
(4) Evaluate the integral
(5) Evaluate the integral
R /3
/6
R
csc3 x dx
cos x
CALCULUS II (PHSCI/ENG) 110.109. HOMEWORK WEEK 02.
Exercise. Evaluate the integral:
Exercise. Evaluate the integral:
Exercise. Evaluate the integral:
Z
(p5 ln p) dp.
Z
x tan2 x dx.
Z
2
t2 sin 2t dt
0
Exercise. Evaluate the integral by making a substitutio
CALCULUS II (ENG) 110.109.
Exercise. Plot the point whose polar coordinates are given. Then find the Cartesian coordinates of the point.
5
5
7
) b) (1,
) c) (2,
)
a) ( 2,
4
2
6
Exercise. Sketch the region in the plane consisting of points whose polar coo
CALCULUS II (PHSCI/ENG) 110.109. HW WEEK 04. STUDENT
COPY
Exercise 1. Evaluate the integral:
Z 2
x +x+1
dx
(x2 + 1)2
Exercise 2. Evaluate the integral:
Z
x2 2x 1
dx
(x 1)2 (x2 + 1)
Exercise 3. Evaluate the integral:
Z 5
x +x 1
dx
x3 + 1
Exercise 4. Make a
Problem 1: Consider a hollow tube of length L, radius R with a uniform charge Q
and with the z-axis as its central axis. What is the electric eld at z0 along the z-axis,
where z0 > L?
To start this problem we can use the idea that there is a line of charg
Problem 1: A 75 MHz radio wave passes from vacuum into an insulating ferrite.
Find the wavelength in vacuum, the wave speed and wavelength in the ferrite, where
K=10.0 and Km =1000.0 at this frequency.
= c/ f
= (3 108 m/s)/(75 106 /s)
=4m
v = c/ KKm
v =
Problem 1: Consider two concentric, conducting spherical shells of radii ra < rb .
The inner shell has charge Q and the outer shell has charge Q. What is the capacitance
between these two shells with and without an insulator with dielectric constant, K, i
Problem 1: Part a: The diagram shows a light ray passing through a slab with index
of refraction n2 submerged in a liquid with an index n1 . What are the relative values of
these indices?
The answer to this multiple choice was a. In this case n1 < n2 beca
Problem 1: A 50 m long aluminum wire is connected across a 12 V battery. What
is the current density inside the wire? ( = 2.75 108 m)
IL
A
I
=
A
= JL
V
=
L
= 8.72 106
V=
J
V
J
J
Problem 2: A long wire is connected across a xed voltage. When the temperatur
Problem 1: Monochromatic light of wavelength 632.8 nm falls on 2 slits separated
by 0.15 mm. On a screen a distance of 9 m away what is the smallest distance from the
center of the central maximum where the intensity is 55% of its maximum.
The intensity a
Problem 1: When monochromatic light is passed through a diraction grating with
4500 lines/cm, the highest order bright fringe seen is m = 5. What does this imply
about the wavelength of the light? (Note that the m = 5 line is seen but the m = 6 line
is no
For both of these problems we want to combine Kirchos Laws, resistors in
parallel and AC circuits.
Z1 =
Z2 =
1
C
R2 +
1
2
(1)
R2 + (L)2
2
(2)
Z1 Z2
Z1 + Z2
(3)
Z=
The rst two are the impedance for the two lines. The last equation treats the two lines
like
Problem 1: A solenoid has a 3 cm by 3 cm square cross-section, 225 turns and a
length of 70 cm. The current through the solenoid varies as I(t) = 5t3 4t2 10 (in
A). At t = 2 s what are the energy stored in the solenoid and the voltage across the
solenoid?
Problem 1: Oxygen-16 is a nucleus with 8 protons and 8 neutrons. The force on
an electron due to an Oxygen-16 nucleus has a magnitude of 3.5 1014 N. What is the
distance between the electron and the Oxygen-16 nucleus?
Coulombs Law gives us
kq1 q2
.
(1)
F=
Problem 1: A solid, insulating sphere of radius, R, has a charge density, (r) =
r
0 (1 ( R )4 ).
Part a: What is the Electric Field as a function of radius?
This is a problem similar to what was done before only here, the charge density is
not uniform. Sy
Problem 1: Consider a long wire along the x-axis with a current of 15A in the negative x-direction.
Part a: What is the magnetic eld (vector) at the position (-5cm,4cm,0)?
0 I
The magnetic eld near a long straight current carrying wire is given by B = 2r
Problem 1: A at coil has an 18 cm radius, 40 turns and a total resistance of 40 m.
If this coil sits in the xy-plane in a magnetic eld with a z-component that decreases at
a rate of 12 T/s (dBz /dt=-12 T/s), then what is the magnitude of the induced curre