Answer Q.13, Q.14 and Q.15 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 v. A uniform electric field E and a uniform magnetic field B exist everywhere. The velocity v, electric field E and magnetic field B are given in columns 1, 2 and 3, respectively. The quantities E₀, B₀ are positive in magnitude.
Column 1 — (I) Electron with v = 2(E₀/B₀)x^; (II) Electron with v = (E₀/B₀)ŷ; (III) Proton with v = 0; (IV) Proton with v = 2(E₀/B₀)x^Column 2 — (i) E = E₀ẑ; (ii) E = −E₀ŷ; (iii) E = −E₀x^; (iv) E = E₀x^Column 3 — (P) B = −B₀x^; (Q) B = B₀x^; (R) B = B₀ŷ; (S) B = B₀ẑ
In which case will the particle describe a helical path with axis along the positive z direction?