A charged particle is introduced at the origin $x = 0, y = 0, z = 0$ 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 a uniform magnetic field $\vec{B}$ are given in the columns below

Column 1 Column 2 Column 3

1. Electron with $\vec{v} = 2 \frac{E_{0}}{B_{0}} \hat{x}$ (i) $\vec{E} = E_{0} \hat{z}$ (P) $\vec{B} = - B_{0} \hat{x}$

2. Electron with $\vec{v} = \frac{E_{0}}{B_{0}} \hat{y}$ (ii) $\vec{E} = - E_{0} \hat{y}$ (Q) $\vec{B} = B_{0} \hat{x}$

3.Proton with $\vec{v} = 0$ (iii) $\vec{E} = {- E}_{0} \hat{x}$ (R) $\vec{B} = B_{0} \hat{y}$

4. 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 describe a helical path with axis along positive z direction?

Question

Important Questions on Magnetic Effects of Current and Magnetism

Column 1	Column 2	Column 3
1. Electron with $\vec{v} = 2 \frac{E_{0}}{B_{0}} \hat{x}$	(i) $\vec{E} = E_{0} \hat{z}$	(P) $\vec{B} = - B_{0} \hat{x}$
2. Electron with $\vec{v} = \frac{E_{0}}{B_{0}} \hat{y}$	(ii) $\vec{E} = - E_{0} \hat{y}$	(Q) $\vec{B} = B_{0} \hat{x}$
3.Proton with $\vec{v} = 0$	(iii) $\vec{E} = {- E}_{0} \hat{x}$	(R) $\vec{B} = B_{0} \hat{y}$
4. Proton with $\vec{v} = 2 \frac{E_{0}}{B_{0}} \hat{x}$	(iv) $\vec{E} = E_{0} \hat{x}$	(S) $\vec{B} = B_{0} \hat{z}$