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1.2 6) Two particle guns shoot particles into an area where there is a perpendicular uniform magnetic field B. The dashed lines show the tracks of these particles in and out of the area. a) Determine the polarity of the charges (positive or negative?) b) if the ratio of the charges is -1 and the positively charged particle i massive than the other one, find the ratio vi/v2. 2 times more

1.2 6) Two particle guns shoot particles into an area where there is a perpendicular uniform magnetic field B. The dashed lines show the tracks of these particles in and out of the area. a) Determine the polarity of the charges (positive or negative?) b) if the ratio of the charges is -1 and the positively charged particle i massive than the other one, find the ratio vi/v2. 2 times more

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
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Example Problem 6: Motion of Charged Particles in a Magnetic Field #### Problem Statement: Two particle guns shoot particles into an area where there is a perpendicular uniform magnetic field \( B \). The dashed lines show the tracks of these particles in and out of the area. a) Determine the polarity of the charges (positive or negative). b) If the ratio of the charges is -1 and the positively charged particle is 2 times more massive than the other one, find the ratio \( v_1/v_2 \). --- #### Diagram Explanation: The diagram provides a visual representation of the problem: - The area where the particles move is enclosed by a rectangular boundary, and a uniform magnetic field \(\vec{B}\) is present (denoted by red crosses indicating the direction of the field perpendicular to the plane of the page, into the page). - Two particle guns are labeled as 1 and 2: - The first particle gun projects a particle with initial velocity \( \vec{v}_1 \) to the left. - The second particle gun, placed at a distance of \( \frac{R}{2} \) from the first, projects a particle with initial velocity \( \vec{v}_2 \) upward. - The paths of the particles are curved, as shown by dashed lines: - Particle 1 follows a semicircular path to the left, indicating a clockwise curvature. - Particle 2 follows a semicircular path downward, indicating a counterclockwise curvature. --- #### Solutions: a) **Determine the Polarity of the Charges:** - According to the right-hand rule for the motion of charged particles in a magnetic field: - For a positive charge: the thumb points in the direction of velocity \(\vec{v}\), fingers point in the direction of \(\vec{B}\) (into the page), and the palm indicates the force direction (curvature of the path). - For a negative charge: the force direction is opposite to the palm's direction. - For Particle 1, the path curves to the right (clockwise), suggesting that the force responsible for the curvature is directed towards the center of the circular path. Applying the right-hand rule implies that the particle is negatively charged. - For Particle 2, the path curves downward (counterclockwise), suggesting that the force responsible is directed towards the center of the circular path. Applying the right-hand rule implies
Transcribed Image Text:### Example Problem 6: Motion of Charged Particles in a Magnetic Field #### Problem Statement: Two particle guns shoot particles into an area where there is a perpendicular uniform magnetic field \( B \). The dashed lines show the tracks of these particles in and out of the area. a) Determine the polarity of the charges (positive or negative). b) If the ratio of the charges is -1 and the positively charged particle is 2 times more massive than the other one, find the ratio \( v_1/v_2 \). --- #### Diagram Explanation: The diagram provides a visual representation of the problem: - The area where the particles move is enclosed by a rectangular boundary, and a uniform magnetic field \(\vec{B}\) is present (denoted by red crosses indicating the direction of the field perpendicular to the plane of the page, into the page). - Two particle guns are labeled as 1 and 2: - The first particle gun projects a particle with initial velocity \( \vec{v}_1 \) to the left. - The second particle gun, placed at a distance of \( \frac{R}{2} \) from the first, projects a particle with initial velocity \( \vec{v}_2 \) upward. - The paths of the particles are curved, as shown by dashed lines: - Particle 1 follows a semicircular path to the left, indicating a clockwise curvature. - Particle 2 follows a semicircular path downward, indicating a counterclockwise curvature. --- #### Solutions: a) **Determine the Polarity of the Charges:** - According to the right-hand rule for the motion of charged particles in a magnetic field: - For a positive charge: the thumb points in the direction of velocity \(\vec{v}\), fingers point in the direction of \(\vec{B}\) (into the page), and the palm indicates the force direction (curvature of the path). - For a negative charge: the force direction is opposite to the palm's direction. - For Particle 1, the path curves to the right (clockwise), suggesting that the force responsible for the curvature is directed towards the center of the circular path. Applying the right-hand rule implies that the particle is negatively charged. - For Particle 2, the path curves downward (counterclockwise), suggesting that the force responsible is directed towards the center of the circular path. Applying the right-hand rule implies
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