# A particle of mass m and charge q moves with a constant velocity v along the positive x direction. It enters a region containing a uniform magnetic field B directed along the negative z direction, extending from x = a to x = b. The minimum value of v required so that the particle can just enter the region  x>b  is Option 1) $\frac{qbB}{m}$ Option 2) $\frac{q\left ( b-a \right )B}{m}$ Option 3) $\frac{qaB}{m}$ Option 4) $\frac{q\left ( b+a \right )B}{2m}$

V Vakul

As we learnt in

$r=\frac{mv}{qB}=\frac{P}{qB}=\frac{\sqrt{}2mk}{qB}=\frac{1}{B}\sqrt{}\frac{2mV}{q}$

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For particle to enter x > b

Radius $\geq$ (b - a)

$\Rightarrow \frac{mv}{qB}\geq b-a$   or       $v \geq \frac{qB(b-a)}{m}$

$v^{min}=\frac{qB(b-a)}{m}$

Option 1)

$\frac{qbB}{m}$

incorrect

Option 2)

$\frac{q\left ( b-a \right )B}{m}$

correct

Option 3)

$\frac{qaB}{m}$

incorrect

Option 4)

$\frac{q\left ( b+a \right )B}{2m}$

incorrect

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