The Figure Shows a Mass Spectrograph That Is Operated with Deuterons

The figure shows a mass spectrograph that is operated with deuterons, which have a charge of $+ e$ and a mass of $3.34 \times 10 ^ { - 27 } \mathrm {~kg}$ . The deuterons emerge with negligible velocity from the source, which is grounded. The speed of the deuterons as they pass through the accelerator grid is $8.0 \times$ $10 ^ { 5 } \mathrm {~m} / \mathrm { s }$ . A uniform magnetic field of magnitude $B = 0.20 \mathrm {~T}$ , directed out of the plane, is present to the right of the grid and is perpendicular to the velocity of the deuterons. The deuterons make a circular orbit in the magnetic field. What is the radius of this orbit, and what is the initial direction of their deflection just as they enter the magnetic field? $\left( e = 1.60 \times 10 ^ { - 19 } \mathrm { C } \right)$

A) $71 \mathrm {~mm}$ , upward
B) $69 \mathrm {~mm}$ , downward
C) $62 \mathrm {~mm}$ , upward
D) $62 \mathrm {~mm}$ , downward
E) $84 \mathrm {~mm}$ , downward

Correct Answer:

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