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Does the time spent by a charged particle inside a dee of a cyclotron depend upon its speed and the radius of its path ? Why ? |
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Answer» The time spent by a charged particle to describe a semicircular path of radius r inside a dee of a cyclotron is independent of the radius of the path and the speed v so long as the mass m of the particle is constant. This is true for any charged particle of mass m and carrying a charge q, and is the critical characteristic of operation of the cyclotron. r = \(\cfrac{mv}{qB}\) So that the time spent in a dee, t = \(\cfrac{\pi r}v\) = \(\cfrac{\pi }v\) x \(\cfrac{mv}{qB}\) = \(\cfrac{\pi m}{qB}\) which is independent of r and v. |
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