InterviewSolution
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InterviewSolution
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Obtain expression for the radius of the circular path and its frequency, of a charged particle entering into an uniform magnetic field. |
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Answer» Solution :Let B represent the uniform magnetic applied perpendicular to the plane of the paper and pointing inwards. Let q represents a +ve charge entering the field with a velocity v at right angles to the field. Let F represent the magnetic force on the charged particle, which ACTS perpendicular to the direction of velocity. No WORK is done by the force. Magnetic force `vec(F)=qvec(v) times vec(B)`. This force acts as a CENTRIPETAL force and produces a circular motion (as per the Fleming's Left Hand Rule).  i.e., `""(mv^(2))/r=qvBsin90^(@)` i.e., `""r=(mv)/(qB)` Therefore, radius of the circular PATH `r propto m/q` for a given uniform speed and magnetic field. Period of revolution `T=(2pir)/v=(2pim)/qB " and frequency " v=l/T=(qB)/(2pim)` In the presence of the component of velocity along B, the path described by the charged particle will be helix and whose pitch `p=v_(h)T, v_(h)` is the horizontal component of velocity along B. 
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