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?

Question

TuteeHUB · Accepted Answer

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

TuteeHUB · Answer

$${{v}_{x}}\hat{i}+{{v}_{y}}\hat{j}+\frac{e}{m}{{v}_{y}}B\,t\,\hat{k}$$

TuteeHUB · Answer

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

TuteeHUB · Answer

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

1.	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.	\[{{v}_{x}}\hat{i}+\left( {{v}_{y}}+\frac{e}{m}{{v}_{y}}B\,t\, \right)\hat{i}+{{v}_{y}}\hat{j}\]
Answer» B. \[{{v}_{x}}\hat{i}+{{v}_{y}}\hat{j}-\frac{e}{m}{{v}_{y}}B\,t\,\hat{k}\]

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