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) $\to B = - B_{0}^x$

(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 would the particle move in a straight line along the negative direction of $y$ -axis (i.e, move along $-^y) ?$

(IV) (ii) (S)

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(III) (ii) (P)

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(III) (ii) (R)

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(II) (iii) (Q)

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Solution

The correct option is C (III) (ii) (R)
In a given situation we need to find the velocity in negative $y$ direction.

For option 1:
Here, initially partical is moving in x-diraction, so he is not able to move in y-direction.
hence, this option is wrong.

For option 2:
if initial velocity is zero and electric field is in negative y-direction and magnetic field at negative z- direction, so the partical is going to continually move in negative z-direction.
Hence, this option is also wrong.

for option 3:
if initial velocity is zero and electric field is in negative y-direction and magnetic field at positive y direction, so the partical is going to continually move in negative y direction.

So, option C is correct.

For option 4:
Here, initial velocity is in y-direction and direction of electric field is in negative x-directio where as, magnetic field is in also negative x-direction. So, partical will not move in y-direction.
so, this option is also wrong.

From above solution option C is correct.

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Similar questions

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) $\to B = - B_{0}^x$
(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?

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 $\to v = 2 \frac{E_{0}}{B_{0}}^x$	$(i)$ $\to E = E_{0}^z$	$(P)$ $\to B = - B_{0}^x$
$(I I)$ 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) $\to B = B_{0}^z$