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Consider the mass spectrometer shown schematically in the figure below. The magnitude of the electric field between the plates of the velocity selector is 2.60  103 V/m, and the magnetic field in both the velocity selector and the deflection chamber has a magnitude of 0.0300 T. Calculate the radius of the path for a singly charged ion having a mass m = 2.58  10-26 kg.

Consider the mass spectrometer shown schematically in the figure below. The magnitude of the electric field between the plates of the velocity selector is 2.60  103 V/m, and the magnetic field in both the velocity selector and the deflection chamber has a magnitude of 0.0300 T. Calculate the radius of the path for a singly charged ion having a mass m = 2.58  10-26 kg.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Consider the mass spectrometer shown schematically in the figure below. The magnitude of the electric field between the plates of the velocity selector is 2.60  103 V/m, and the magnetic field in both the velocity selector and the deflection chamber has a magnitude of 0.0300 T. Calculate the radius of the path for a singly charged ion having a mass m = 2.58  10-26 kg.

 

 

### Diagram Explanation for Educational Website The image illustrates a setup involving a velocity selector and a magnetic field to analyze charged particles. Here's a detailed explanation of the components and their interactions: 1. **Velocity Selector:** - The velocity selector comprises perpendicular electric (\(\vec{E}\)) and magnetic (\(\vec{B}_{\text{in}}\)) fields. - These fields are oriented such that a charged particle \(q\) moving through the selector experiences forces from both fields. 2. **Charged Particle:** - A positively charged particle, \(q\), enters the velocity selector with a velocity \(\vec{v}\). - The electric field, \(\vec{E}\), applies a force upward (due to the negative to positive plate configuration shown in red and blue). - The magnetic field, \(\vec{B}_{\text{in}}\), applies a force downward, opposing the electric force. 3. **Balanced Forces and Velocity Selection:** - When the electric and magnetic forces balance (\(qE = qvB_{\text{in}}\)), the particle travels in a straight line, exiting the velocity selector without deviation. 4. **Path in Magnetic Field:** - After passing through the velocity selector, the particle enters a magnetic field, \(\vec{B}_{0, \text{in}}\), perpendicular to its velocity and pointing into the plane (represented by crosses). - This causes the particle to move in a circular path due to the magnetic force acting as a centripetal force. 5. **Detector Array:** - The particle's trajectory is bent until it hits the detector array at point \(P\). - The detector array measures the position \(\vec{r}\) of the impacting particle, helping determine its properties such as velocity and charge-to-mass ratio. This setup is often used in experiments to measure specific properties of particles by exploiting the interactions of electric and magnetic fields.
Transcribed Image Text:### Diagram Explanation for Educational Website The image illustrates a setup involving a velocity selector and a magnetic field to analyze charged particles. Here's a detailed explanation of the components and their interactions: 1. **Velocity Selector:** - The velocity selector comprises perpendicular electric (\(\vec{E}\)) and magnetic (\(\vec{B}_{\text{in}}\)) fields. - These fields are oriented such that a charged particle \(q\) moving through the selector experiences forces from both fields. 2. **Charged Particle:** - A positively charged particle, \(q\), enters the velocity selector with a velocity \(\vec{v}\). - The electric field, \(\vec{E}\), applies a force upward (due to the negative to positive plate configuration shown in red and blue). - The magnetic field, \(\vec{B}_{\text{in}}\), applies a force downward, opposing the electric force. 3. **Balanced Forces and Velocity Selection:** - When the electric and magnetic forces balance (\(qE = qvB_{\text{in}}\)), the particle travels in a straight line, exiting the velocity selector without deviation. 4. **Path in Magnetic Field:** - After passing through the velocity selector, the particle enters a magnetic field, \(\vec{B}_{0, \text{in}}\), perpendicular to its velocity and pointing into the plane (represented by crosses). - This causes the particle to move in a circular path due to the magnetic force acting as a centripetal force. 5. **Detector Array:** - The particle's trajectory is bent until it hits the detector array at point \(P\). - The detector array measures the position \(\vec{r}\) of the impacting particle, helping determine its properties such as velocity and charge-to-mass ratio. This setup is often used in experiments to measure specific properties of particles by exploiting the interactions of electric and magnetic fields.
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