Cathode Ray Tube (CRT) style televisions use a capacitor to accelerate electrons

Question

Cathode Ray Tube (CRT) style televisions use a capacitor to accelerate electrons (with a small hole in the positively charged plate, to allow the electrons to pass through), then a magnetic field to steer the electrons towards precise locations on the screen. A schematic of this arrangement is shown below. This particular CRT uses a 10 kV "accelerating voltage" (meaning the capacitor is charged to 10 kV, and that is what is used to speed up the electron from rest to a particular final speed as it leaves the capacitor). First, determine how fast the electrons are going when they exit the capacitor. Then determine what the strength of the magnetic field should be to produce a deflection of 10 degree. The magnetic field exists only in a region 2 cm by 2 cm - so the electron travels 2 cm to the right while its path is being bent by the magnetic field. Keep in mind that you found in activity 31 that a charged particle moving at constant speed through a uniform B field will move along a circular path (and you determined the radius of that path). Once the electron leaves the capacitor, the electric field drops to zero - so it will no longer be accelerating due to the capacitor. Also, the magnetic force is always perpendicular to the motion - which means the magnetic force can not do any work on the electron, so that will also not change its speed. So the electron moves at constant speed through the B field, along a circular path. The main trick here is the geometry involved - sketch out the full circular path that the electron would move in if the magnetic field continued indefinitely, and also sketch out the radius of that circle.

Explanation / Answer

as potential difference of 10 KV is applied to accelerate the electron, energy gained by it will 10 KeV which will be equal to 1.6*10-15 joule. so speed of the electron when it enters into magnetic field can be given by -

0.5 mv2 = E

v = 5.92*107

so force exerted by magnetic field, F = qvB sin 90

F = 9.47*10-12 B

ma = F

a = 1.04*1019 B

as speed of electron does not get changed in horizontal direction-

t = 0.02/v

t = 3.37*10-10 sec

s = ut + 0.5 at2

as u = 0

tan 10 = s/2

s = 0.35 cm

0.35/100 = 0.5*a*t2

a = 6.16*1016 m/sec2

B = 5.92 mT

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