An electron in a cathode ray tube is accelerated through a...

An electron in a cathode ray tube is accelerated through a potential difference of 10 kV, then passes through the 2 cm wide region of uniform magnetic field as shown in figure. What field strength will deflect the electron by 10°? Steps: (a) Using conservation of energy, find the velocity at which electron enters the magnetic field. (b) Using geometry, show that radius of the cyclotron motion $r = \frac{2cm}{sin10°}$ (c) The radius of the cyclotron motion is given by $r = \frac{mv}{qB}$. Find the magnetic field.

Transcript

00:01 So let's say electrons are initially given a kinetic energy of 600 electron volts, and they're entering into a region with a magnetic field presence.

00:13 So part a asks, what's the velocity of these electrons? so first let's convert this.

00:18 600 electron volts comes out to about 9 .6 times 10 to the negative 17th joules.

00:28 So the speed of these electrons is going to be the square root of.

00:31 2k over m and so this comes out to about 1 .45 times 10 to the seventh meters per second and then part b says they enter into or let's change the speed so now the new speed is 10 to the 7th meters per second what radius circle these electrons move if the magnetic field of 10 millie tesla is applied to them so what we have is the mass of the electron times the velocity squared, divided by its race.

01:13 This is like our centripetal force, is equal to the charge of an electron.

01:17 It's called it e times the velocity times the magnetic field.

01:20 And so we can see that the radius is going to be the charge of an electron times the magnetic field divided by the momentum of the electrons.

01:29 So this is 1 .6 times 10 to the negative 19th kulams times 0 .01 .1.

01:38 Tesla over our electrons mass which is 9 times 10 to the negative 31st 9 .11 times in the negative first 31st times 10 to the 7 meters per second so if you do that we should get something like 175 .63 meters and then part c asks so if the electrons are traveling to the right meaning like if they go upwards and then oh sorry i have this backwards if the electrons are initially traveling to the right and the magnetic field is applied into the page like this and what direction are they going to be deflected and if used the right -hand rule you'll see basically downwards initially they'll go in a circular path downwards because they're negatively charged so you get the opposite direction of what you use it in the right -hand rule and then part d, what electric field would be required to cancel the magnetic field deflection? so what we have is the charge of the electron times the electric field...

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