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Electricity and Magnetism

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Moderate

Change of Radius of Circulating Charge with Kinetic Energy

EANDM-E5BHYZ

A mass analyzer is sketched on the accompanying figure. A box containing a magnetic field $B$, pointed into the plane of the drawing, has a entrance slit in which a particle of mass $m_o$ and charge $-|q |$ enters. The particle is emitted from plate (a) which is at a potential of $-V_0$ relative to the potential of plate (b) and the box, both of which are at ground ($V=0)$. The particle circulates in the magnetic field, and exits the box at a distance $x_o$ from the entrance.

If the accelerating potential on plate 'a' were changed to $V=-2V_o$, what would be the new position $x$ of the particle's exit (in terms of the original $x_o$)?

A

$x=\cfrac{x_o}{2}$

B

$x = 4 \, x_o$.

C

$x = x_o$.

D

$x = \sqrt{2} \, x_o$.