A charged particle (electron or proton) is introduced at the origin (x=0,y=0,z=0) with a given initial velocity $\overrightarrow{\nu }$ . A uniform electric field $\overrightarrow{E}$  and a uniform magnetic field $\overrightarrow{B}$ exist everywhere. The velocity $\overrightarrow{\nu }$ , electric field $\overrightarrow{E}$  and magnetic field $\overrightarrow{B}$  are given in columns 1,2 and 3, respectively. The quantities  $E_0$,$B_0$  are positive in magnitude.
Column 1	Column 2	Column 3
(I) Electron with $\overrightarrow{\nu }=2\frac{E_0}{B_0}\widehat{x}$	(i) $\overrightarrow{E}=E_0\widehat{z}$	(P) $\overrightarrow{B}=-B_0\widehat{x}$
(II) Electron with $\overrightarrow{\nu }=\frac{E_0}{B_0}\widehat{y}$	(ii) $\overrightarrow{E}=-E_0\widehat{y}$	(Q) $\overrightarrow{B}=B_0\widehat{x}$
(III) Proton with $\overrightarrow{\nu }=0$	(iii) $\overrightarrow{E}=-E_0\widehat{x}$	(R) $\overrightarrow{B}=B_0\widehat{y}$
(IV) Proton with $\overrightarrow{\nu }=2\frac{E_0}{B_0}\widehat{x}$	(iv) $\overrightarrow{E}=E_0\widehat{x}$	(S) $\overrightarrow{B}=B_0\widehat{z}$

In which case will the particle describe a helical path with axis along the positive z direction?

• A

  (II) (ii) (R)

• B

  (III) (iii) (P)

• C

  (IV) (i) (S)

• D

  (IV) (ii) (R)