The figure below shows a schematic diagram of a mass spectrometer. A charged particle enters a velocity selector, in which a uniform electric field E (created by charged plates) points to the right, and a magnetic field Bin points into the page. Upon exiting the velocity selector, the particle enters a deflection chamber with a magnetic field Bo, in- The particle travels a semicircular path until it hits a photographic plate at point P. Assume the particle is a singly charged lon with mass m = 2.08 x 10-26 kg. The magnitude of the electric field is 945 V/m, and the magnitude of both the magnetic field in the velocity selector and in the deflection chamber is 0.925 T. What is the radius r (in m) of the particle's path in the deflection chamber? X x X x x $ x P Bo.in X x x Photographic plate X xxx Bin x x 30 Velocity selector x x x x x x E X x XI F x X x X x x x x (

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Chapter1: Units, Trigonometry. And Vectors
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The image presents a schematic diagram of a mass spectrometer. A charged particle enters a velocity selector, where a uniform electric field \(\vec{E}\) (created by charged plates) is directed to the right, and a magnetic field \(\vec{B}_{\text{in}}\) points into the page. After exiting the velocity selector, the particle moves into a deflection chamber with a magnetic field \(\vec{B}_{0, \text{in}}\). The particle follows a semicircular path until it reaches a photographic plate at point \(P\).

The diagram includes the following components:
- **Velocity Selector**: Consists of parallel plates with electric and magnetic fields. Arrows indicate that \(\vec{E}\) points to the right, and \(\vec{B}_{\text{in}}\) is directed into the page.
- **Deflection Chamber**: Shows the particle’s trajectory as a semicircle under the influence of the magnetic field \(\vec{B}_{0, \text{in}}\), which also points into the page.
- **Photographic Plate**: Positioned where the particle's path ends, marking point \(P\).

The problem asks to assume the particle is singly charged with a mass \(m = 2.08 \times 10^{-26}\) kg. The electric field \(\vec{E}\) has a magnitude of 945 V/m, and the magnetic fields in both the velocity selector and the deflection chamber have magnitudes of 0.925 T. The question is to determine the radius \(r\) (in meters) of the particle's path in the deflection chamber.
Transcribed Image Text:The image presents a schematic diagram of a mass spectrometer. A charged particle enters a velocity selector, where a uniform electric field \(\vec{E}\) (created by charged plates) is directed to the right, and a magnetic field \(\vec{B}_{\text{in}}\) points into the page. After exiting the velocity selector, the particle moves into a deflection chamber with a magnetic field \(\vec{B}_{0, \text{in}}\). The particle follows a semicircular path until it reaches a photographic plate at point \(P\). The diagram includes the following components: - **Velocity Selector**: Consists of parallel plates with electric and magnetic fields. Arrows indicate that \(\vec{E}\) points to the right, and \(\vec{B}_{\text{in}}\) is directed into the page. - **Deflection Chamber**: Shows the particle’s trajectory as a semicircle under the influence of the magnetic field \(\vec{B}_{0, \text{in}}\), which also points into the page. - **Photographic Plate**: Positioned where the particle's path ends, marking point \(P\). The problem asks to assume the particle is singly charged with a mass \(m = 2.08 \times 10^{-26}\) kg. The electric field \(\vec{E}\) has a magnitude of 945 V/m, and the magnetic fields in both the velocity selector and the deflection chamber have magnitudes of 0.925 T. The question is to determine the radius \(r\) (in meters) of the particle's path in the deflection chamber.
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