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Question I: Consider region of space containing magnelic field given by B = 12 i uT . An electron is launched into the field at velocity of v = 1.6x 106 [ + 12x 106...

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Question I: Consider region of space containing magnelic field given by B = 12 i uT . An electron is launched into the field at velocity of v = 1.6x 106 [ + 12x 106 j m/s. Calculate the radius of the helical path traced out by the electron and the cyclotron frequency. Give your answers in centimeters and Megahertz, respectively:

Question I: Consider region of space containing magnelic field given by B = 12 i uT . An electron is launched into the field at velocity of v = 1.6x 106 [ + 12x 106 j m/s. Calculate the radius of the helical path traced out by the electron and the cyclotron frequency. Give your answers in centimeters and Megahertz, respectively:



Answers

An electron enters a region of magnetic field of mag. nitude $0.0100 \mathrm{~T}$, traveling perpendicular to the linea? boundary of the region. The direction of the field is per pendicular to the velocity of the electron. (a) Determine the time it takes for the electron to leave the "field-filled" region, noting that its path is a semicircle. (b) Find the kinetic energy of the electron if the radius of its semicircular path is $2.00 \mathrm{~cm}$.

Given that an electron enters a region of magnetic hill magnetic field of magnitude the post 20.100 Tesla. And search of an electron defended by Q. Is supposed to reno minus 1.6 to 10 to the power 19 column and must off and electron and it's equal stew 9.11 and took 10 to the Power -31. The lava. Mhm. When an electron enters a region of magnetic field then the magnitude of magnetic force equals thus interpreted acceleration. Therefore magnetic force physicals to em into the square upon our where Evista magnetic force and MR MAs of direct on this is the ferocity artista. There it is negative fools is perpendicular to the both of the velocity of the child's Q. And magnetic field. Therefore Magnificence of indigenous you in to be into being this is equal to and we took his square one. Therefore R. S. Equals to em into P upon you. Yeah it's not that He is equals two You into being who you are up one. And let's say this is equation number a distance table by electron E. Is equals two. Buy into hi for semi santa. No, the time taken for the electrons to move in the part of cemetery. That is time T. Is equal to E. What the where is that time? And this is the distance. Therefore the is I into our a point here because it was too, I am too. He art is it is And in two p upon you'll be yeah. BNP get cancer. So this is equal stupid. Right? Mm into Q B which is right. Mm. No such as you think that values. Therefore why is 3.14 Into mass is 9.11 into 10. to the power -31 telegram divided by Q. Is 1.6 Into 10 to the par -19. Well, uh into These 1010. So this is equal, stupid Can be 8.605 ft divided by 1016 into 10. To the power minus do it. So this is equal to 1.787 into 10. to the power -9 second. This can be written as one 792 tend to depart my last night. Second be that ideas of semicircular part are a sequel stew. Mhm. Why in geology? Don't send meter which is equal to 0.02 m. The kinetic energy of electron as it goes to, you know, 1.2 into em into the square must this must into velocity square. Uh huh. This is the goods to 112 into mm B. S. Q. in two G. Into art one of them square. This is from equation number so sure, none. But what? This is a good strip one up one. Um Into you square. You too. The square into our square. Have food the secret skip. Uh huh. Into Q. Square. Into the square. Into our square upon them. No substituting the values. So this is a good school. Oh into Q. Square is 1.6 And 10 to the Power -19. Well um square into the zero point. You don't want you don't you know that's not yeah, radius is given that it's zero point. You know, we did square divided by M. S. 9.118- 10 to the Power -31 kg. Therefore. Uh huh and do 2.56 into the point. You know, you know, you know one into to the point. But you don't point. You know you look cool Into 10 to the -38 Divided by 9.1, 1 to 10 to the minus what to have this. You know, point hi into do you know point you know what, you know Cheeto? Cheeto? Cheeto? Cheeto. Okay, well 10-4 Divided by 9.11 into 10 to the Car -7. So this is supposed to did of wine right into 1.12 food into 10 to the power minus 50. So this is supposed to you don't point right? So you know, point pipe six To into 10 to the minus 15. This is the good stuff, right .6-2 10 to the Power -16. Sure, now converting this into electron balls, we get we get kinetic energy. This equates to 5.62 into 10 to the power -16, june Divided by 1.6 to 10 to the power minus 19 electron board. This is a good student, see point like one To into 10 to the power see electron book. This can be the Tennis three point 51 gay bi.

Okay. First step is to equate the component of, um, magnetic field s so it's entering at an angle. Fate also, that could magnetic for a component of the magnetic force. She's making the component forces Q B B signed data, and that is equal to a centripetal force M V squared over R Therefore, our is, uh, oops. Are is envy. Sign data over Q B. So mass of a proton is one of an electron. His 9.11 times 10 to the negative. 31 kilograms. 31 there velocity is three times 10 of the six meters per second times sign 45 degrees over Q elementary charge 1.6 times 10 to the negative 19. Pardon my handwriting there 1.6 times 10 to the negative 19 cool ums Times be, which has 0.23 Tesla. And so this gives us a radius off 5.25 times 10 to the negative five meters. Now the period, um, the the period of oscillation of circular motion is two pi R over. Beep up over the perpendicular velocity, which is view you signed data. We're just gonna write us be perpendicular and so to pi over the perpendicular times are, which is m times v perpendicular over q B. So the perpendicular cancel and two comes out to be two pi over Q B and now the final step, which has pitched p cost of velocity. So it will be vey parallel this time. You parallel times the time period tea, and so this is vey co sign for a five times to you, which we just found to two pi over Q B. Now replacing Values V is three times two of the six units per second times Co. Sign 45 times to pie over elementary charge. 1.6 times 10 of 19 cool homes times magnetic field strength pointing to three Tesla. This gives you a pitch off 3.3 times 10 to the negative four meters.

Well, we have a centripetal force, which is m. We scrape the body by our right, which is equal to the magnetic force, which is cute times three times be right. No, let's sold for R So our physical too. 9.11 times 10 to the dollar, minus 31 into 0.92 times the speed of light all square divided by 0.92 times the speed of light multiplied by 1.6 times 10 to the power minus 31 into one point. It so odd is equal to, um, 0.872 meter.

Hi problem here is. And accelerating potential difference We is equal to 100 all The magnitude of magnetic at this 0.2. This stuff The charged particles are excavated with the help of the security defense and then these charged particles are allowed to move perpendicular to this magnetic field. So they will describe circular paths in the magnetic field. Pens for an electron radius of that party described by the electron the magnetic field. I thought it is going as and we buy you. We consider this envy as a momentum linear momentum of the electron and write it like this. And then we know a relation between the in your momentum and kinetic energy. That is two times of the product of mass of the charged particle. It's kinetic energy invited by Big You and finally or the kinetic energy he may use. It is equal to a product of charge the particle, the potential difference with which it has been the treaty. So finally plugging in all known values here. This is quite route of price of mass of the charged particle and the charged particle here is electron. This is 9.1 in two Advantant for -31 kg. Then charged over an electron 1.16 to 10 for -19. The potential this is that gold and divided by Magetically 2.2 Multiplied again. Electronic charge with 1.6 Into 10 for- mine included. You're the new military. It will be 2,912 and this will be taken out Leaving behind a bandage for -25 out of the room And in denominator it will be 0.32 and reform minus I mean well finally this radius, know what it is. 168.6 10 for -6 m. Or we can stay its radius is 120169 and a meter. Which is the answer for the first part of this problem. Now, The 2nd part of the problem in this second part of the problem, this electron is replaced by protons. So put on. There will be only a single the mass of the proton, which is 1.67 into 10 for -27. Yeah, So now the really is given by using the same expression But a different value of Mars 1.67 10 for -27 kg deployed by the charge over a proton, which is same as that of electron 1.6 into Spanish for minus in and multiplied by potential difference. It is spill and it gold divided by his Eagle point dume to electronic Protonix charge, which is 1.16- 24 months. Yeah. Finally, here it will be The numerator. This is 534 0.4 Taken out to engage for -23. Why did Why 0.32 into 10 Dish 1? That's mm. Finally, the serious here will come out with 0.72. Then you need answer for the second part of this problem. Thank you.


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