TAP 518-7: Fields in nature and in particle accelerators

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1 TAP - : Field in nature and in particle accelerator Intruction and inforation Write your anwer in the pace proided The following data will be needed when anwering thee quetion: electronic charge 9 C a of electron 9 3 kg ε 0 9 F Quetion Suppoe that a thundercloud ha a flat horizontal bae of area k The bae of the cloud i 00 aboe the Earth urface o that a unifor electric field i fored between the cloud and the Earth A field of 0 between the bae of the cloud and the Earth i ufficient to caue a lightning flah Calculate the potential difference between the cloud and the ground at the oent the lightning flah begin The charge on the bae of the cloud i gien by the forula Q ε 0 A E where A i the area of the bae of the cloud and E i the electric field trength between the bae and the Earth Calculate the charge on the bae of the cloud 3 The cloud and the Earth can be thought of a a parallel plate capacitor that tore energy when charged Auing that the potential difference iediately after the flah i ery all copared with the potential difference at the beginning of the flah, calculate a alue for the energy releaed during the flah Electron accelerated through a potential difference of 00 enter a unifor agnetic field of 000 T perpendicular to the direction of otion 4 Calculate the peed of the electron when they enter the agnetic field

2 Ue your anwer to quetion 4 to calculate the radiu of the orbit in the agnetic field In an electron tube, electron were paed through a region containing a ertical electric field E and a horizontal agnetic field B When the force on the electron were balanced the electron paed through the tube undeflected horizontal agnetic field undeflected path of electron ertical electric field Show that the electron of charge e pa undeflected when they hae a elocity E/B The eparation of the deflector plate wa 4 and no deflection wa obered when the oltage acro the plate wa 3 k and the agnetic field wa 3 T Calculate the elocity of the electron The oltage ued to accelerate the electron to thi elocity wa 0 Ue your anwer to quetion to calculate the ratio e/ for electron where i the a of an electron

3 A proton joined to a neutron i known a a deuteron or deuteriu ion and i ued in nuclear cattering experient A deuteron ha a a of 33 kg and a charge of + 9 C 9 Calculate the oltage required to accelerate a deuteron fro ret in a acuu to a elocity of 9 (3% of the peed of light In an early for of particle accelerator, deuteron were ade to oe in a circular path within a toroidal tube of diaeter A toroidal tube i like a hollow ring 0 Calculate the agnetic field required to contrain a deuteron within the tube at the elocity of 9 Hint 4 The charge and a of the electron are gien in the Intruction and inforation The electric and agnetic force are equal in agnitude You will need to change the unit before calculating the electric field trength You will need to conider the equation for the electron gun ued to accelerate the electron 9 You are ued to calculating the peed of electron when accelerated The a of a deuteron i not the ae a the a of an electron 0 The quetion gie the diaeter of the orbit and not the radiu

4 Practical adice In quetion and there are eeral tage in the calculation o exceie rounding in the earlier part of the quetion would lead to error in the final anwer All anwer hae been rounded to two ignificant figure, but three ignificant figure hae been ued for nuerical alue that hae been carried through to the next tage of the calculation Anwer and worked olution Ed 0 00 Q ε AE 0 (9 9 C F (000 3 Q 9 C ( 9 J 4 e o e ( C 00 kg 39 4 Be / r o r Be 0 04 ( kg ( 39 T ( 9 C ee Be o E / B

5 E d E B 33 3 T 3 e o e (3 0 C kg 9 q o q (33 kg (9 ( 9 C 4 0 Bq / r o B qr 0 3 T ( 3 3 ( kg ( 9 9 C 0 External reference Thi actiity i taken fro Adancing Phyic chapter, 0S

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