A charged particle (electron or proton) is introduced at the origin (ð¥ = 0, ð¦ = 0, ð§ = 0) with a given initial velocity vecv. A uniform electric field vecE and a uniform magnetic field vecB exist everywhere. The velocity vecv, electric field vecE and magnetic field vecB are given in columns 1, 2 and 3, respectively. The quantities ð¸0 , ðµ0 are positive in magnitude. Column 1 Column 2 Column 3 (I) Electron with vecv=2 (E0/B0) hatx (i) vecE=-E0 hatz (P) vecB=-B0 hatx (II)Electron with vecv= (E0/B0) haty (ii) vecE=-E0 haty (Q) vecB=-B0 hatx (III) Proton with vecv=0 (iii) vecE=-E0 hatx (R) vecB=-B0 haty (IV)Proton with vecv=2 (E0/B0) hatx (iv) vecE=-E0 hatx (S) vecB=-B0 hatz In which case will the particle describe a helical path with axis along the positive ð§ direction?

Question

A charged particle (electron or proton) is introduced at the origin (ð¥ = 0, ð¦ = 0, ð§ = 0) with a given initial velocity vecv. A uniform electric field vecE and a uniform magnetic field vecB exist everywhere. The velocity vecv, electric field vecE and magnetic field vecB are given in columns 1, 2 and 3, respectively. The quantities ð¸0 , ðµ0 are positive in magnitude. Column 1 Column 2 Column 3 (I) Electron with vecv=2 (E0/B0) hatx (i) vecE=-E0 hatz (P) vecB=-B0 hatx (II)Electron with vecv= (E0/B0) haty (ii) vecE=-E0 haty (Q) vecB=-B0 hatx (III) Proton with vecv=0 (iii) vecE=-E0 hatx (R) vecB=-B0 haty (IV)Proton with vecv=2 (E0/B0) hatx (iv) vecE=-E0 hatx (S) vecB=-B0 hatz In which case will the particle describe a helical path with axis along the positive ð§ direction? (A) (IV) (i) (S) (B) (II) (ii) (R) (C) (III) (iii) (P) (D) (IV) (ii) (R)

Tardigrade Admin · Accepted Answer

In option (D), particle moves in a circle in x - y plane without the electric field. With vec E it is lifted up (along the z direction) with constant acceleration generating a helix with constant radius and increasing pitch.

Column 1	Column 2	Column 3
(I) Electron with $v = 2 \frac{E _{0}}{B _{0}} \overset{x}{^}$	(i) $E = - E_{0} \overset{z}{^}$	(P) $B = - B_{0} \overset{x}{^}$
(II)Electron with $v = \frac{E _{0}}{B _{0}} \overset{y}{^}$	(ii) $E = - E_{0} \overset{y}{^}$	(Q) $B = - B_{0} \overset{x}{^}$
(III) Proton with $v = 0$	(iii) $E = - E_{0} \overset{x}{^}$	(R) $B = - B_{0} \overset{y}{^}$
(IV)Proton with $v = 2 \frac{E _{0}}{B _{0}} \overset{x}{^}$	(iv) $E = - E_{0} \overset{x}{^}$	(S) $B = - B_{0} \overset{z}{^}$

(IV) (i) (S)

(II) (ii) (R)

(III) (iii) (P)

(IV) (ii) (R)

In option (D), particle moves in a circle in x−y plane without the electric field. With E it is lifted up (along the z direction) with constant acceleration generating a helix with constant radius and increasing pitch.

In option (D), particle moves in a circle in $x - y$ plane without the electric field. With $E$ it is lifted up (along the z direction) with constant acceleration generating a helix with constant radius and increasing pitch.