Solution to practice test problem 912wavelength of am

Solution to Practice Test Problem 9.12(Wavelength of AM Radio)
Problem: You wish to build a very long wavelength radio transmitter. If the target wavelength is 1000m , at
what frequency should your transmitter operate?
(a) 3 . 3 × 10
- 6
Hz
(b) 4 . 8 × 10
4
Hz
(c-Answer) 3 . 0 × 10
5
Hz
7

(d) 1 . 9 × 10
6
Hz
(e) Toby.
Solution
The wavelength is related to the frequency by c = λf , therefore
f =
c
λ
=
3 × 10
8m
s
1000m
= 3 . 0 × 10
5
Hz
Total Points for Problem: 3 Points
Solution to Practice Test Problem 9.13(Energy Stored in LHC)
Problem: The ATLAS detector at the Large Hadron Collider uses a superconducting magnet to bend charged
particles into circular tracks. At the operating current of 21 , 000A the magnet stored 1 . 1 × 10
9
J of energy. What
is the inductance of the superconducting solenoid used for the magnet?
Select One of the Following:
Total Points for Problem: 3 Points
Solution to Practice Test Problem 9.14(Ampere’s Law with Copper Pipe)
Problem: A co-axial cable is constructed from two co-axial conductors. The inner conductor is a wire running
down the axis of the outer conductor. Let the inner conductor carry current I out of the page and be modeled
as infinitely thin. The outer conductor is a cylindrical tube with inner radius a = 0 . 20mm and an outer radius
b = 0 . 25mm . If the tube is long compared to its radius, it can be modeled as an infinite cylindrical conductor.The
current I flows down the tube such that the current is uniformly distributed through the tube. The current in the
tube flows into the page. An end view of the system is drawn below.
(a)Draw the magnetic field in all regions.
(b)Calculate the magnetic field symbolically in all regions.
(c)Let I = 0 . 15A . What is the magnetic field at a point P at - 0 . 10mmˆx as drawn below? Let the origin
be along the center of the wire. Report the field as a vector.
8

I
II
III
a
b
P
y
x
wire
tube
Solution to Part (a)
A total current out of the page is encircled in regions I and II
producing a counter-clockwise field, by the right-hand rule. The
total current encircled in region III is zero, so the field in region
III is zero.
I
II
III
Air
Air
y
x
wire
Grading Key: Part (a) 3 Points
Solution to Part (b)
(a) Compute B
I
: In region I, the total current enclosed by a path of radius r for 0 < r < a is
I
enc
= I
Therefore, by substituting into the general expression for the magnetic field of a wire, the magnetic field in region
I is
vector
B
I
=
μ
0
I
2 πr
counter-clockwise
9