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Non-relativistic protonsmoverectinearly in the region of space where thereare unifrommutually perpendicularelectric and magneticfieldswith E = 4.0 kV//m and B = 50 mT. The trajectory of the protons lies in the plates xz (Fig) and formsan anglevarphi = 30^(@) with the x axis. Findteh pithcof the helical trajectoryalongwhich theprotonswill moveafter the electricfield is swiched off. |
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Answer» Solution :When the ELECTRIC field is swichted off, the path followed by theparticlewill be helical. And pitch, `Delta l = v_(|\|) T`, (where `v_(|\|)` is the velocity of the particle, parallel to `vec(B)`, and `T`, the time PERIOD of revolution.) `= v cos (90 - varphi) T = v sin varphi T` `= v sin varphi (2pi m)/(aB)` (as `T = (2pi)/(qB)`) ...(1) Now, when both the FIELDS were present , `qE = qvB sin (90 - varphi)`, as no net force was EFFECTIVE on the SYSTEM. or, `v = (E)/(B cos varphi)` ....(2) From (1) and (2), `Delta l =v (E)/(B) (2pi m)/(qB) tan varphi = 6 cm`. |
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