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

Question

By appropriately matching the information given in the three columns of the following table. 
A charged particle (electron or proton) is introduced at the origin (x = 0, y = 0, z = 0) with a given initial velocity  vector v . A uniform electric field vector E  and a uniform magnetic field vector B exist everywhere. The velocity vector v,  electric field vector E  and magnetic field vector B  are given in columns 1, 2 and 3, respectively. The quantities E₀, B₀ are positive in magnitude.

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

(A) (IV) (i) (S) 

(B) (II) (ii) (R) 

(C) (III) (iii) (P) 

(D) (IV) (ii) (R)

Answer 1

The force due to magnetic field F_B will provide the necessary centripetal force for circular motion which will be in X-Y plane. The force due to electric field will accelerate proton in Z-direction. Thus the path will be helical with increasing pitch.