Question ID - 174485 | SaraNextGen Top Answer
A particle of mass $m$ and charge $q$, moving with velocity $V$ enters Region II normal to the boundary as shown in the figure. Region II has a uniform magnetic field $B$ perpendicular to the plane of the paper. The length of the Region II is $l$.
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1.(a) The particle enters Region III only if its velocity
$
V>\frac{q B}{m}
$
(b) The particle enters Region III only if its velocity
$
V<\frac{q l B}{m}
$
(c) The particle enters Region III only if its velocity
$
V=\frac{q l B}{m}
$
(d) All of the above
2.Path length of the particle in Region II is maximum when
(a) velocity $V=\frac{q l B}{2 m}$
(b) velocity $V=\frac{2 q l B}{m}$
(c) velocity $V=\frac{q l B}{m}$
(d) velocity $V=\frac{4 q l B}{m}$
3.Time spent in Region II as long as the particle returns to Region I is
(a) two times if velocity $V$ is doubled
(b) halved if velocity is doubled
(c) halved if velocity is halved
(d) same for any value of $V$
4.If the direction of the initial velocity of the charged particle is neither along nor perpendicular to that of the magnetic field, then the orbit will be
(a) a straight line
(b) an ellipse
(c) a circle
(d) a helix
5.A charged particle moves with velocity $\vec{V}$ in a uniform magnetic field $\vec{B}$. The magnetic force experienced by the particle is
(a) always zero
(b) never zero
(c) zero, if $\vec{B}$ and $\vec{V}$ are perpendicular
(d) zero, if $\vec{B}$ and $\vec{V}$ are parallel
a)a,c,d,d,d b)b,c,d,d,d c)a,c,d,c,d d)a,c,d,d,c
We know that $r=\frac{m V}{q B}$
$
\therefore \quad V>\frac{q B l}{m}
$
(a) If $r>l$ then particle enter the III region $\frac{m V}{q B}>l$
(c) If $V=\frac{q B l}{m}$ then particle will cover semi circular path in this condition the path length of the particle in region II is maximum.
(d) Time spent in region II, $T=\frac{\pi m}{q B}$
It does not depends upon the velocity.
(d) a helix
(d) $F=q(\vec{V} \times \vec{B})$ if $V \| B$, then $\vec{F}=0$
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