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A particle enters a space where exists uniform magnetic field \( \vec{B}=B_{x} \vec{i}+B_{y} \vec{j}+B_{z} \vec{k} \) \& uniform electric field \( \vec{E}=E_{x} \vec{i}+E_{y} \vec{j}+E_{z} \vec{k} \) with initial velocity \( \vec{u}=u_{x} \vec{i}+u_{y} \vec{j}+u_{z} \vec{k} \). Depending on the values of various components the particle selects a path. Match the entries of column A with the entries of column B. The components other than specified in column A in each entry are non-zero. Neglect gravity.
\begin{tabular}{|l|l|l|l|}
\hline & \multicolumn{1}{|c|}{ Column I } & & \multicolumn{1}{|c|}{ Column II } \\
\hline (A) & \begin{tabular}{c}
\( B_{y}=B_{z}=E_{x}=E_{z}=0 \) \\
\( u=0 \)
\end{tabular} & (P) & Circle \\
\hline (B) & \begin{tabular}{l}
\( E=0, u_{x} B_{x}+u_{y} B_{y} \) \\
\( \neq-u_{z} B_{z} \)
\end{tabular} & (Q) & \begin{tabular}{l}
Helix with uniform \\
pitch and constant \\
radius
\end{tabular} \\
\hline (C) & \( \vec{u} \times \vec{B}=0, \vec{u} \times \vec{E}=0 \) & (R) & Cycloid \\
\hline (D) & \( \vec{u} \perp \vec{B}, \vec{B} \| \vec{E} \) & (S) & \begin{tabular}{l}
Helix with uniform \\
pitch and variable \\
radius
\end{tabular} \\
\hline & & (T) & Unknown curve \\
\hline & & (U) & \begin{tabular}{l}
Helix with variable \\
pitch and constant \\
radius
\end{tabular} \\
\hline
\end{tabular}
\begin{tabular}{lllll}
& A & B & C & D \\
(1) & \( \mathrm{R} \) & \( \mathrm{Q}, \mathrm{V} \) & \( \mathrm{V} \) & \( \mathrm{U} \) \\
(2) & \( \mathrm{S} \) & \( \mathrm{P}, \mathrm{T} \) & \( \mathrm{Q} \) & \( \mathrm{T} \) \\
(3) & \( \mathrm{R} \) & \( \mathrm{Q}, \mathrm{S} \) & \( \mathrm{P} \) & \( \mathrm{Q} \) \\
(4) & \( \mathrm{R} \) & \( \mathrm{Q}, \mathrm{T} \) & \( \mathrm{V} \) & \( \mathrm{U} \)
\end{tabular}


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