A charged particle (electron or proton) is introduced at the origin (x = 0, y = 0, z = 0) with a given initial velocity . A uniform electric field and a uniform magnetic field exist everywhere. The velocity , electric field and magnetic field are given in columns 1, 2 and 3, respectively. The quantities E0, B0 are positive in magnitude.Column 1Column 2Column 3(I) Electron with (i) (P) (II) Electron with (ii) (Q) (III) Proton with (iii) (R) (IV) Proton with (iv) (S)

A charged particle (electron or proton) is introduced at the origin (x = 0, y = 0, z = 0) with a given initial velocity $\vec{ν}$ . A uniform electric field $\vec{E}$ and a uniform magnetic field $\vec{B}$ exist everywhere. The velocity $\vec{ν}$ , electric field $\vec{E}$ and magnetic field $\vec{B}$ are given in columns 1, 2 and 3, respectively. The quantities E₀, B₀ are positive in magnitude.

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

Linked Question 1

In which case will the particle move in a straight line with constant velocity ?

(IV) (i) (S)

(III) (ii) (R)

(III) (iii) (P)

(II) (iii) (S)

F_electro = q × E = – q E₀ x

F_net = E_Electro + F_magnetic = 0

Hence particle will move along straight line

Linked Question 2

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

(IV) (ii) (R)

(II) (ii) (R)

(III) (iii) (P)

(IV) (i) (S)

Force and velocity are perpendicular to each other.

Linked Question 3

In which case would the particle move in a straight line along the negative direction of y-axis (i.e., move along – $\overset{⌢}{y}$ )?

(II) (iii) (Q)

(III) (ii) (P)

(III) (ii) (R)

(IV) (ii) (S)

$\vec{F} = qvB = q (\vec{v} \times \vec{B})$

$\vec{F} = q \vec{E}$