A) \[\frac{2{{E}^{2}}{{t}^{2}}}{mq}\]
B) \[\frac{{{E}^{2}}{{q}^{2}}{{t}^{2}}}{2m}\]
C) \[\frac{E{{q}^{2}}m}{2{{t}^{2}}}\]
D) \[\frac{Eqm}{2t}\]
Correct Answer: B
Solution :
Force the charged particle \[F=qE\] \[\therefore \] Acceleration \[a=\frac{qE}{m}\] From relation \[\upsilon =u+at\] or \[\upsilon =0+\frac{qEt}{m}\] \[\upsilon =\frac{qEt}{m}\] Kinetic energy \[=\frac{1}{2}m{{\upsilon }^{2}}\] \[=\frac{1}{2}m\frac{{{q}^{2}}{{E}^{2}}{{t}^{2}}}{{{m}^{2}}}\] \[=\frac{{{q}^{2}}{{E}^{2}}{{t}^{2}}}{2m}\]
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