A particle of mass m and charge q is thrown at a speed u in the region of uniform electric field E. The particle's initial velocity is in direction opposite to direction of electric field. Determine the time in which the particle reaches its projection position.

Asked by rishabhkaushik2000 | 30th Dec, 2015, 05:48: PM

Expert Answer:

A charged particle moving parallel to the electric field will experience an acceleration if the electric force acting on it is in its direction of travel or a deceleration if the electric force acting on it is in the opposite direction of travel.
The particle's initial velocity in opposite direction of electric field, the charged particle will first undergo deceleration (its speed becomes slower), begin mathsize 12px style straight v space equals space straight u space minus at subscript 1 space space space left parenthesis negative space straight a space due space to space particle space will space first space undergo space deceleration right parenthesis straight t subscript 1 equals fraction numerator straight u minus straight v over denominator straight a end fraction space Now comma space particle space stops comma space and space then space undergo space acceleration. space Hence comma space straight v space becomes space intial space velocity space and space straight v apostrophe space be space final. straight v apostrophe space equals space straight v space minus at subscript 2 space space straight t subscript 2 equals fraction numerator straight v minus straight v apostrophe over denominator straight a end fraction space the space time space in space which space the space particle space reaches space its space projection space position space is space straight T straight T space equals space straight t subscript 1 plus straight t subscript 2 space space straight T equals fraction numerator straight u minus straight v over denominator straight a end fraction space plus fraction numerator straight v minus straight v apostrophe over denominator straight a end fraction equals 1 over straight a open square brackets straight u minus straight v apostrophe close square brackets Substituting space value space of space straight a straight T equals straight m over qE open square brackets straight u minus straight v apostrophe close square brackets end style.
F = q E
F = m a
q E = m a
begin mathsize 12px style straight a equals qE over straight m end style
The particle's initial velocity in opposite direction of electric field, the charged particle will first undergo deceleration
substituting in the kinematic equation gives
 

Answered by Priyanka Kumbhar | 31st Dec, 2015, 05:55: PM

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