Find the approximate deflection of the beamdue to this magnetic field. ( Hint: P

Question

Find the approximate deflection of the beamdue to this magnetic field. (Hint: Place the origin at thecenter of the electron beam’s arc and compare an undeflectedbeam’s path to the deflected beam’s path.) In the electron gun of a TV picture tube the electrons (charge - e , mass m )are accelerated by a voltage V .After leaving the electron gun, the electron beam travels adistance D to the screen; in this region there is a transverse magnetic fieldof magnitude B and no electric field. Find the approximate deflection of the beamdue to this magnetic field. (Hint: Place the origin at thecenter of the electron beam's arc and compare an undeflectedbeam's path to the deflected beam's path.) Express your answer in terms of thevariables B , D , e , m ,and V .

Explanation / Answer

Speed of the electron after pass through Voltage V is   v = [ 2 V e / m ] This electron enter into magnetic field B and travel adistance D . In Horizonatl direction : ----------------------- distance travel = D velocity v = v time t = t from the relation time = distance / velocity                              t = D / v In vertical direction : -------------------- Initial velocity u = 0 time t = D / v displacement S = y acceleration a = force /mass                     = B v e / m from the relation   S = ut + ( 1/ 2) a t ^ 2                            y = ( 1/ 2) ( B ve / m ) ( D /v ) ^ 2                               = ( 1/ 2)( B D 2 e ) / ( m v )

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