Download Chapter 30

Chapter 29
The Magnetic Field
Objectives:
1.
To understand the properties of a magnetic field
2.
To understand the combined effect of an electric and a magnetic field on a
charged particle (the Lorentz force):
3.
4.
5.
F  q E  qv  B
To understand the motion of a particle in a magnetic field.
R
mv
qB

qB
m
To understand the application of the Lorentz force to various devices:
E
B
A.
Velocity selector v 
B.
Mass spectrometer R 
C.
Cyclotron
D.
Magnetic Mirrors and Bottles
v max 
mv
qB
qBR
m
To understand the magnetic force exerted on a wire with current
dF  I d  B
F  I L B
6.
To understand the torque exerted on a current loop
  N I A Bsin 
   B
Chapter 29 Problems
1.
A particle carrying a 50 C charge moves with a velocity v = 5 i + 3.2 k m/s
through a uniform magnetic field B = - 9.4 i + 6.7 j T. What is the force on the
particle?
2.
A magnetic field of .1 T points in the x-direction. A charged particle carrying 1
C enters the field region moving at 20 m/s. What are the magnitude and
direction of the force on the particle when it first enters the region if it does so
moving (a) along the x-axis; (b) along the y-axis; and (d) at 45 ° to both the x and
y-axes?
3.
Electrons and protons, accelerated through the same potential difference, enter a
region of uniform magnetic field, moving perpendicular to B. (a) Compare their
kinetic energies. (b) Compare their orbital radii.
4.
The Van Allen belts are regions in space where high energy charged particles are
trapped in the earth’s magnetic field. If the field strength at the Van Allen belts is
.1 G, what are the period and radius of the helical path described by a proton with
1 MeV kinetic energy?
5.
In a certain cyclotron, a proton moves in a circle of radius .5 m. The magnitude of
the magnetic field is 1.2 T. (a) What is the cyclotron frequency and kinetic energy
of the proton (in eV)?
6.
What is the force on a 50 cm long wire carrying 15 A at right angles to a 500 G
magnetic field?
7.
A 10 cm long wire with a mass 2.2 g is suspended by a pair of flexible leads as
shown. If there is a magnetic field of .5 T pointing into the page, what are the
magnitude and direction of the current required to remove the tension in the
supporting leads?
10 cm
8.
A single turn loop 10 cm in diameter carries a current of 12 A. It experiences a
torque of 0.15 N m when the normal to the loop plane makes a 25 ° angle with a
uniform magnetic field. What is the magnetic field strength?