question_answer

An electron, charge?e, mass m, enters a uniform magnetic field \[\overset{\to }{\mathop{B}}\,=B\overset{\to }{\mathop{i}}\,\] with an initial velocity \[\overset{\to }{\mathop{v}}\,={{v}_{x}}\overset{\to }{\mathop{i}}\,+{{v}_{y}}\overset{\to }{\mathop{j}}\,\]. What is the velocity of the electron after a time interval of t second?

A) \[{{v}_{x}}\hat{i}+{{v}_{y}}\hat{j}+\frac{e}{m}{{v}_{y}}B\,t\,\hat{k}\]        

B) \[{{v}_{x}}\hat{i}+{{v}_{y}}\hat{j}-\frac{e}{m}{{v}_{y}}B\,t\,\hat{k}\]

C) \[{{v}_{x}}\hat{i}+\left( {{v}_{y}}+\frac{e}{m}{{v}_{y}}B\,t\, \right)\hat{j}\]  

D) \[{{v}_{x}}\hat{i}+\left( {{v}_{y}}+\frac{e}{m}{{v}_{y}}B\,t\, \right)\hat{i}+{{v}_{y}}\hat{j}\]