498 9 Particle Physics – I
9.68 A 10 GeV proton is directed toward the centre of the earth when it is at dis-
tance of 10^3 earth radius away. Through what mean transverse magnetic field
(assumed uniform) must it move if it is to just miss the earth?
9.69 A proton of kinetic energy 20 keV enters a region where there is uniform elec-
tric field of 500 V/cm, acting perpendicularly to the velocity of the proton.
What is the magnitude of a superimposed magnetic field that will result in no
deflection of the proton?
[University of Manchester]
9.70 A particle of known charge but unknown rest mass is accelerated from rest by
an electric fieldEinto a cloud chamber. After it has traveled a distanced,it
leaves the electric field and enters a magnetic fieldBdirected at right angles
toE. From the radius of curvature of its path, determine the rest mass of the
particle and the time it had taken to traverse the distance d.
[University of Durham]
9.71 A proton accelerated to 500 keV enters a uniform transverse magnetic field of
0.51 T. The field extends over a region of spaced=10 cm thickness. Find
the angleαthrough which the proton deviates from the initial direction of its
motion.
9.72 An electron is projected up, at an angle of 30◦with respect to thex-axis, with a
speed of 8× 105 m/s. Where does the electron recross thex-axis in a constant
electric field of 50 N/C, directed vertically upwards?
9.73 A proton moving with a velocity 3× 105 ms−^1 enters a magnetic field of 0.3 T,
at an angle of 30◦with the field. What will the radius of curvature of its path
be (e/m for proton≈ 108 Ckg−^1 )?
9.74 What energy must a proton have to circle the earth at the magnetic equator?
Assume a 1 G magnetic field.
9.75 The average flux of primary cosmic rays over earth’s surface is approxi-
mately 1 cm−^2 s−^1 and their average kinetic energy is 3 GeV. Calculate the
power delivered to the earth from cosmic rays in giga watts. (Earth’s radius
= 6 ,400 km)
9.76 Kaons with momentum 25 GeV/c and deflected through a collimator slit at a
distance of 10 m from a bending magnet 1.5 m long which produces a field of
1.2 T. What should be minimum width of the slit so that it accepts particles of
momenta within 1% of the central value?
9.2.11 Betatron..........................................
9.77 The orbit of electrons in a betatron has a radius of 1m. If the magnetic field
in which the electrons move is changing at the rate of 50 W m−^2 s−^1 , calculate
the energy acquired by an electron in one rotation. Express your answer in
electron volts.
[University of New Castle 1965]