A charged particle is projected with velocity $\to v = u^i$ from the origin, in a region having electric field $\to E$ and magnetic field $\to B$ both. Value of $\to B$ and $\to E$ are given in column 1 and column 2 respectively and path of the particle is given in column 3.

$\begin{matrix} Column 1 & Column 2 & Column 3 (Magnetic field) & (Electric field) & (Path of particle) (i) & \to B = 0 & (i) & \to E = 0 & (P) & Circular path (i i) & \to B = B_{0}^i + B_{0}^j & (i i) & \to E = E_{0}^i & (Q) & Helical path (i i i) & \to B = B_{0}^j + B_{0}^k & (i i i) & \to E = B_{0} u (^j -^k) & (R) & Cycloid (i v) & \to B = B_{0}^k & (i v) & \to E = E_{0}^k & (S) & Straight line \end{matrix}$

Which of the following combination is correct?

(II) (ii) (R)

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(II) (i) (Q)

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(IV) (i) (S)

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None of these

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Solution

The correct option is B
(II) (i) (Q)

If a charged particle with constant velocity enters in a constant magnetic field and the components of velocity of the charged particle are along as well perpendicular to the magnetic field then the path of the charged particle is helical.

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A charged particle is projected with velocity $\to v = u^i$ from the origin, in a region having electric field $\to E$ and magnetic field $\to B$ both. Value of $\to B$ and $\to E$ are given in column 1 and column 2 respectively and path of the particle is given in column 3.

$\begin{matrix} Column 1 & Column 2 & Column 3 (Magnetic field) & (Electric field) & (Path of particle) (i) & \to B = 0 & (i) & \to E = 0 & (P) & Circular path (i i) & \to B = B_{0}^i + B_{0}^j & (i i) & \to E = E_{0}^i & (Q) & Helical path (i i i) & \to B = B_{0}^j + B_{0}^k & (i i i) & \to E = B_{0} u (^j -^k) & (R) & Cycloid (i v) & \to B = B_{0}^k & (i v) & \to E = E_{0}^k & (S) & Straight line \end{matrix}$

In which of the following combination particle moves with uniform speed?

In which of the following combination particle moves in uniform circular motion?

Q. A charged particle with some initial velocity is projected in a region where non-zero electric and/or magnetic fields are present. In column I, information about the existence of electric and/or magnetic field and direction of initial velocity of charged particle are given; while in Column II, the probable path of the charged particle is mentioned. Match the entries of Column I with the entries of Column II.

\begin{matrix} Colum I & Colum II i. & \to E = 0, \to B \neq 0 and initial velocity may & a. & Straight line be at any angle with \to B . ii. & \to E = 0, \to B = 0 and initial velocity may & b. & Parabola be at any angle with \to E . iii & \to E \neq 0, \to B \neq 0, \to E | | \to B and initial velocity is & c. & Circular ⊥ to both. d. & Helical path \end{matrix}

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

Column 1	Column 2	Column 3
$(I)$ Electron with $\to v = 2 \frac{E_{0}}{B_{0}}^x$	$(i)$ $\to E = E_{0}^z$	$(P)$ $\to B = - B_{0}^x$
$(I I)$ Electron with $\to v = \frac{E_{0}}{B_{0}}^y$	$(i i)$ $\to E = - E_{0}^y$	$(Q)$ $\to B = - B_{0}^x$
$(I I I)$ Electron with $\to v = 0$	$(i i i)$ $\to E = - E_{0}^x$	$(R)$ $\to B = B_{0}^y$
$(I V)$ Electron with $\to v = 2 \frac{E_{0}}{B_{0}}^x$	$(i v)$ $\to E = E_{0}^x$	$(S)$ $\to B = B_{0}^z$

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

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

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

z

direction?

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The correct option is B (II) (i) (Q) If a charged particle with constant velocity enters in a constant magnetic field and the components of velocity of the charged particle are along as well perpendicular to the magnetic field then the path of the charged particle is helical.

The correct option is B
(II) (i) (Q)

If a charged particle with constant velocity enters in a constant magnetic field and the components of velocity of the charged particle are along as well perpendicular to the magnetic field then the path of the charged particle is helical.