Projectile motion of a particle of mass M with charge Q is projected with an initial speed V in a driection opposite to a uniform electric fiedl of magnitude E.

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Question:

projectile motion of a particle of mass M with charge Q is projected with an initial speed V in a driection opposite to a uniform electric fiedl of magnitude E.

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Answer:Range, [tex]R = MV²/2QE[/tex]Explanation:The question deals with the projectile motion of a particle mass M with charge Q, having an initial speed V in a direction opposite to that of a uniform electric field. Since we are dealing with projectile motion in an electric field, the unknown variable here, would be the range, R of the projectile. We note that the electric field opposes the motion of the particle thereby reducing its kinetic energy. The particle stops when it loses  all its kinetic energy due to the work done on it in opposing its motion by the electric field. From work-kinetic energy principles, work done on charge by electric field = loss in kinetic energy of mass.So, [tex]QER = MV²/2{/tex} where R is the distance (range) the mass moves before it stopsTherefore {tex}R = MV²/2QE{/tex}

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