Download Magnetic exam fill-in

Magnetic exam fill-in
I will add points from this to your magnetism exam up to a score of 85 points. If you
scored higher than 85, I won’t grade this.
A How do we measure magnetic fields?
Consider a horizontal rectangular metallic bar
carrying an electric current in the long direction
and placed in a vertical magnetic field as shown at
right. Assume the metal has a density of movable
electrons = n electrons/m3 which move through
the metal with drift velocity v.
(a) Which direction are the electrons in the metal
moving? [2 points]
(b) Describe the force on the moving electrons with an equation and identify the direction
of the force on them. [4 points]
(c) What would be the result of such a force on the location of the electrons, assuming it
is strong enough? Remember the electrons cannot leave the metal. [3 points]
(d) As this process continues, an equilibrium situation occurs (very quickly) in which the
magnetic field’s force on the moving electrons is balanced by an electric force. Write an
expression for this force in terms of a field. [2 points]
(e) Write an equation showing the force balance in the equilibrium condition.
{Be careful about signs for the directions here!} [3 points]
(f) We often measure voltage as an output, as we do in this case. Rewrite one of your
fields in terms of voltage. [2 points]
(g) Use the electron density, n, to write an expression for the total number of mobile
electrons in the metal piece. Then write an expression for the current in terms of this
result, charge e, velocity and other needed variables. {The current is given in Amps
(C/s), check your units.} [5 points]
(h) Now put these together to get an expression for the voltage across the width of the
metal bar in terms of the current I, magnetic field B and the density of mobile electrons,
n. [5 points]
This result expresses the voltage measured in a probe used to measure the magnetic field
perpendicular to the metal bar. Our magnetic field probes work this way.
B The Earth’s magnetic field varies from about 30μT in equatorial regions to around
60μT near the poles. Charged particles from the Sun and other sources, such as
supernovae are continually bombarding the Earth. A typical particle of this type would
be a proton with an energy of 100 GeV.
From our discussion while studying relativity, this energy is equal to the mass energy
plus the kinetic energy: 100GeV = γMpc2 where Mp is the mass of a proton and
γ=1/√[(1-(v/c)2]. For the proton, Mpc2 = 1 GeV approximately.
(a) Given this information, calculate the velocity of a 100GeV proton. [3 points]
(b) If this proton enters the magnetic field at an angle of 60º to the magnetic field,
calculate the force on the particle from the magnetic field near the equator and near the
pole. Assume the angle stays the same for both locations. [6 points]
(c) Using the force from (b) and the component of the velocity perpendicular to the field,
calculate the radius of the orbit of the proton around the magnetic field lines for both the
equator and the pole. The expression for centripetal force is F = mv2/r. The mass of a
proton in kg can be found on the inside front cover of your book. [6 points]
(d) Remembering that there is still a component of the velocity parallel to the field,
describe the path of these protons in the Earth’s field. [4 points]