A particle of mass and charge , moving with velocity enters Region II normal to the boundary as shown in the figure. Region II has a uniform magnetic field perpendicular to the plane of the paper. The length of the Region II is . Choose the correct cho

Question

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 $ℓ$ . Choose the correct choice(s). [2008]

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(1, 3, 4)

As $V ⊥ B$ and $B$ is uniform, the path of the charged particle in region-II is circular and the radius of the circular path is $r = \frac{m v}{q B}$

For the particle to enter region III, $r > ℓ$ (path shown by dashed line)

$\frac{m v}{q B} > ℓ$ $\Rightarrow v > \frac{q ℓ B}{m}$

For maximum path length in region II, $r = ℓ$

$∴$ $ℓ = \frac{m v}{q B}$ $\Rightarrow v = \frac{q ℓ B}{m}$

The time taken by the particle to move in region II before coming back to region I is $t = \frac{T}{2} = \frac{π m}{q B},$

which is independent of $v$ , i.e., the time spent is same in region II is the same for any velocity.

Solution

Q.
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 $ℓ$ . Choose the correct choice(s). [2008]

1 The particle enters Region III only if its velocity $v > \frac{q ℓ B}{m}$

2 The particle enters Region III only if its velocity $v < \frac{q ℓ B}{m}$

3 Path length of the particle in Region II is maximum when velocity $v = \frac{q ℓ B}{m}$

4 Time spent in Region II is same for any velocity $v$ as long as the particle returns to Region I.

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Solution

Q. 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. Choose the correct choice(s). [2008]

1 The particle enters Region III only if its velocity v>qℓBm

2 The particle enters Region III only if its velocity v<qℓBm

3 Path length of the particle in Region II is maximum when velocity v=qℓBm