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  • Electric field and magnetic field in a region of space are given by <img alt="\mathrm{\vec{E}=E_0 \hat{j}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cvec%7BE%7D%3DE_0%20%5

Electric field and magnetic field in a region of space are given by \mathrm{\vec{E}=E_0 \hat{j}}  and  \mathrm{\bar{B}=B_0 \hat{j}} . A particle of specific charge a (charge per unit mass) is released from origin with velocity \mathrm{\vec{V}=V_0 \hat{i}} . The position of particle at any time t is

Option: 1

\mathrm{\overrightarrow{\mathrm{r}}=\frac{\mathrm{V}_0}{\mathrm{~B}_0 \alpha} \cos \left(\mathrm{B}_0 \alpha \mathrm{t}\right) \hat{\mathrm{i}}+\frac{1}{2} \mathrm{E}_0 \alpha \mathrm{t}^2 \hat{\mathrm{j}}+\frac{\mathrm{V}_0}{\mathrm{~B}_0 \alpha} \sin \left(\mathrm{B}_0 \alpha t\right) \hat{\mathrm{k}} }


Option: 2

\mathrm{\overrightarrow{r}=\frac{V_0}{B_0 \alpha} \cos \left(B_0 \alpha t\right) \hat{i}+\frac{1}{2} E_0 \alpha t^2 \hat{j}+\frac{V_0}{B_0 \alpha}\left(1-\sin B_0 \alpha t\right) \hat{k} }


Option: 3

\mathrm{\overrightarrow{r}=\frac{V_0}{B_0 \alpha} \sin \left(B_0 \alpha t\right) \hat{i}+\frac{1}{2} E_0 \alpha t^2 \hat{j}+\frac{V_0}{B_0 \alpha}\left(1-\cos B_0 \alpha t\right) \hat{k}}


Option: 4

None of these


Answers (1)

best_answer

 Y  coordinate \mathrm{ \Rightarrow \frac{1}{2} \frac{q E}{m} t^2 }
 In  x z plane radius \mathrm{=\frac{m V_0}{B_o \alpha} \text { in } x \text { in } y }

Find general coordinate with geometry.

Posted by

Devendra Khairwa

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