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AP Physics 2
12.2 Magnetism and Moving Charges
IntermediateMCQMathematicalProportional Analysis15.5k
A schematic diagram showing the entrance plane and ion trajectories in a mass spectrometer. At the bottom, a horizontal line represents a detector plate with a small gap labeled Slit. Below the slit, an upward arrow indicates the entrance direction of the ions. Above the horizontal line is a uniform region containing six circled dots arranged in two horizontal rows of three, defined once with the label \vec{B} indicating a magnetic field directed out of the page. Two dashed semicircular arcs originate at the slit and curve to the right, terminating on the detector plate. The inner dashed semicircular arc is labeled m_1 and the outer dashed semicircular arc is labeled m_2. A horizontal double-headed dimension arrow between the two landing points on the detector plate is labeled \Delta x. No other labels, lines, text, or axes appear.
Semicircular paths of two isotopes entering a magnetic field with identical kinetic energy.
Two singly ionized isotopes with positive charge \(q\) and masses \(m_1\) and \(m_2\) (where \(m_2 > m_1\)) enter a region of uniform magnetic field \(B\) directed perpendicular to their velocities. Both ions enter through the same slit with the same kinetic energy \(K\) and travel in semicircular paths before striking a detector plate aligned with the entrance slit. Which of the following expressions represents the separation distance \(\Delta x\) between the two impact points on the detector plate?

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