An electron is emitted from the cathode of a CRT and accelerated by a high anode voltage, giving it a velocity of leaving the anode.The electron continues at a constant speed and enters a magnetic field at right angles to its velocity, where it is deflected.The flux density of the magnetic field is 5 102 T .The charge on an electron is 1.6 1019 C .The mass of an electron is 9.1 1031 kg .
Calculate: (i) the force acting on the electron (ii) the radius of the circular path followed by the electron, in the magnetic field.
SAMPLE ANSWER 21C
Using the formula for force of a charged body moving through a magnetic field, making sure all values are in their standard unit: (i)
F qvB (1.6 1019)(4 107)(5 102) 3.2 1013 The force acting on the electron is 3.2 1013 N .
(ii)
F mv2 r Q3.2 1013
(9.1 1031)(4 107)2 r
The radius of the circular path is 4.55 103 m .
EXERCISE 21.1 CATHODE RAY TUBES (Charge on electron
Q1 An electron has 120 eV of kinetic energy. (i) What is its energy measured in joules? (ii) What is its velocity?
Q2 Calculate the velocity of an electron in a CRT when it is accelerated by an anode voltage of 12 kV.
Q3 A beam of electrons enters a uniform magnetic field of flux density 8 T travelling at a speed of at right angles to the direction of the field. Calculate the magnitude of the force on the electrons.
2.2 107 m s1
Q4 An electron emitted from a hot cathode is accelerated through a vacuum by a potential difference of 2 kV. It enters a uniform magnetic field of flux density 5 mT at right angles to the field causing it to travel in a circular path. Calculate: (i) the energy of the electron (ii) the speed of the electron (iii) the force acting on the electron when it enters the field
(iv) the radius of the path of the electron. X-rays
X-RAYS X-rays are electromagnetic radiation of extremely high frequency (short wavelength).
THE ELECTRON 383 Qr
(9.1 1031)(4 107)2 3.2 1013
4.55 103
1.6 1019 C; mass of an electron 9.1 1031 kg.)
