A charged particle (electron or proton) is introduced at the origin (? = 0, ? = 0, ? = 0) with a given initial velocity
$\vec{v}$. A uniform electric field
$\vec{E}$ and a uniform magnetic field
$\vec{B}$ exist everywhere. The velocity
$\vec{v}$, electric field
$\vec{E}$ and magnetic field
$\vec{B}$ are given in columns 1, 2 and 3, respectively. The quantities
$?_0 , ?_0$ are positive in magnitude.
| Column 1 |
Column 2 |
Column 3 |
| (I) Electron with $\vec{v}=2 \frac{E_{0}}{B_{0}}\hat{x}$ |
(i) $\vec{E}=-E_{0}\hat{z}$ |
(P) $\vec{B}=-B_{0}\hat{x}$ |
| (II)Electron with $\vec{v}= \frac{E_{0}}{B_{0}}\hat{y}$ |
(ii) $\vec{E}=-E_{0}\hat{y}$ |
(Q) $\vec{B}=-B_{0}\hat{x}$ |
| (III) Proton with $\vec{v}=0$ |
(iii) $\vec{E}=-E_{0}\hat{x}$ |
(R) $\vec{B}=-B_{0}\hat{y}$ |
| (IV)Proton with $\vec{v}=2 \frac{E_{0}}{B_{0}}\hat{x}$ |
(iv) $\vec{E}=-E_{0}\hat{x}$ |
(S) $\vec{B}=-B_{0}\hat{z}$ |
In which case will the particle move in a straight line with constant velocity?