BACKNEXT 20.51 A \"cathode ray tube\" (CRT), as the me a \"ar ent gets very hot

Question

BACKNEXT 20.51 A "cathode ray tube" (CRT), as the me a "ar ent gets very hot electro s occasionally escape rom t. These electrons an across the metal plates labelled A and B in the diagram. in the e accelerated away fr the ament by applying a potential difference ? plates The electrons pass through a hole in plate B and enter the glass sphere. There they pass between the two horizontal metal "deflection" plates labelled C and D. A potential difference ? Vdet can be applied across these plates, to deflect the beam of electrons. In front of and in back of the glass sphere are two coils, through which current can be run to produce a magnetic field in the region between the deflection plates. The cols are oriented so they both produce magnetic fields into the page in this region. b Oj out of the page k into the page d 0 m zero magnitude

Explanation / Answer

i. as electrons have to be accelerated from A to B, A should be -ve and B should be +ve

hence B has a higher positive charge

ii. dVdef = 0

for dVef ! = 0, the electrons are deflected downwards

hecne direction of electric field is upwards ( as electrons move in direction opposite to that of the electric field)

iii. dVa = 3.7 kV

v = ?

from conservation of energy

0.5*9.1*10^-31*v^2 = 1.6*10^-19*dVa

hence

v = 36070748.551962 m/s = 0.12023582850654 c

iv. n = 320 turns

r = 6 cm

d = 8 cm

i = 0.2 A

B = 2ki *2pir^2 /(r^2 + d^2)^3/2

putting in values

B = 4.5238*10^-6 T

v. dVa = 3.7 kV

distance b.w deflection plates, h = 8 mm

i = 0.2 A

dV del = such that net force on electron beam is 0

hence from the options

a. the electric force and magnetic force are opposite to each other

c. the electric fielce and the magnetic firlce are in equal magnmitude

vi. dVdef = for this case

q*v*B = q*Vdef/h

36070748.551962 *4.5238*10^-6 = Vdef/8*10^-3

hence

Vdef = 1.3054417765669 V

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