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AP Physics 2
12.2 Magnetism and Moving Charges
AdvancedMCQMathematicalConceptual16.2k
A 3D schematic showing a uniform magnetic field B directed along the positive z-axis, represented by three parallel vertical arrows pointing upward labeled B. A positive point charge travels upward in a helical path wrapping around a vertical axis parallel to the z-axis. An initial velocity vector v_0 originates at the charge at an angle theta relative to the z-axis. The vertical distance along the z-axis between two consecutive loops of the helix is labeled as pitch p. No other labels, lines, text, or axes appear.
Helical path of a charged particle in a magnetic field.
Three distinct ions—Ion 1 (\(^{1}\text{H}^+\)), Ion 2 (\(^{2}\text{H}^+\)), and Ion 3 (\(^{4}\text{He}^{2+}\))—are launched with the same speed \(v_0\) into a uniform magnetic field \(\vec{B}\). Each ion's initial velocity vector makes an angle \(\theta\) (\(0^\circ < \theta < 90^\circ\)) relative to the direction of \(\vec{B}\), causing each to travel in a helical path. The masses of \(^{1}\text{H}^+\), \(^{2}\text{H}^+\), and \(^{4}\text{He}^{2+}\) are \(m_0\), \(2m_0\), and \(4m_0\), respectively. Which of the following correctly ranks the helical pitch \(p\) (the linear distance traveled parallel to \(\vec{B}\) during one complete revolution) for the three ions?

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