15.5 One of the steps in the manufacture of nuclear
weapons is the separation of the fissile isotope
of uranium,^235 U (235.05 u), from its cousin(^238) U (238.05 u). The purity of samples of
separated uranium is regularly checked in a
nuclear weapons lab by vaporizing and singly
ionizing the uranium, accelerating the ions and
passing them through a velocity selector into a
mass spectrometer deflection chamber.
Photographic film is placed in the position of
the recording plate. The two isotopes of
uranium will strike the film plate at different locations, and their relative abundance will be indicated by the size and darkness
of the two spots created on the film. The velocity selector is set to pass ions with a speed of 3.43×10^5 m/s, and the magnetic
field in the deflection chamber is 0.750 T. What is the distance d between the locations where the two ions of uranium strike
the photographic plate? (Note that 1 u = 1.66×10í^27 kg.)
m
Section 16 - Helical particle motion in magnetic fields
16.1 A particle of charge q = 2.73×10í^12 C and mass m = 3.32×10í^17 kg enters a uniform magnetic field B of magnitude
9.41×10í^5 T with a velocity v of magnitude 8.34 m/s, and moves in a helix while in the field. The angle between v and B is
84.0°. (a) What is the magnitude vperp of the component of v perpendicular to B? (b) What is the radius of the helix? (c) What
is the magnitude vpar of the component of v parallel to B? (d) What is the pitch of the helix, the distance between adjacent
loops (measured parallel to B)?
(a) m/s
(b) m
(c) m/s
(d) m
Section 17 - Interactive problem: helical particle motion
17.1 Use the simulation in the interactive problem in this section to answer the following questions. (a) If the velocity vector is
initially perpendicular to the magnetic field lines, what is the shape of the resulting path of the particle? (b) If the velocity
vector is initially parallel to the magnetic field lines, what is the shape of the resulting path of the particle?
(a) i. A helix
ii. A zigzag
iii. A circle
iv. A straight line
(b) i. A helix
ii. A zigzag
iii. A circle
iv. A straight line
Section 18 - Magnetic force on a current-carrying wire
18.1 A 15.0 ampere current flows through a 3.75 m section of wire, perpendicular to a 0.250 T magnetic field. What is the
magnitude of the force exerted by the field on the wire section?
N
18.2 A straight current-carrying wire carries a current of 0.250 A. It makes an angle of 30° with a uniform magnetic field of strength
0.0255 T. What is the magnitude of the force per unit length that the field exerts on the wire?
N/m
18.3 A segment of insulated wire 0.032 m long carries a current perpendicular to a uniform magnetic field. The strength of the field
is 0.0055 T. The wire is attached to a spring that lies in a direction perpendicular to both the wire and the field. When a current
is passed through the wire, it stretches the spring by an additional amount ǻx = 4.6×10í^4 m. The spring constant is 0.87 N/m.
What current is passing through the wire?
A
18.4 A long horizontal wire with linear mass density Ȝ = 47.5×10í^3 kg/m carries a current of 0.534 A. The wire is situated so that it
is perpendicular to a uniform, horizontal magnetic field that is just strong enough to levitate the wire against its weight. What is
the strength of the field?
T