3) Two particles of the same mass enter a magnetic field with the same speed and follow the paths shown. X X X X X X X X X X X B = 0.55T X X X X X X X х х X X X X X X X X X X X х х х х х х х х х хах ххххххххх 1 2 <- Detectors X X X X X X velocity 1200 m/s Does the particle with the larger charge reach the detector at position "1" or "2"? Explain. If one of the particles is Fe³+, an ion of mass 9.277 x 10-2³g and charge +3e, find the radius of the particles trajectory.
3) Two particles of the same mass enter a magnetic field with the same speed and follow the paths shown. X X X X X X X X X X X B = 0.55T X X X X X X X х х X X X X X X X X X X X х х х х х х х х х хах ххххххххх 1 2 <- Detectors X X X X X X velocity 1200 m/s Does the particle with the larger charge reach the detector at position "1" or "2"? Explain. If one of the particles is Fe³+, an ion of mass 9.277 x 10-2³g and charge +3e, find the radius of the particles trajectory.
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Chapter1: Units, Trigonometry. And Vectors
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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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![**Magnetic Field Trajectories of Charged Particles**
**Problem Statement:**
Two particles of the same mass enter a magnetic field with the same speed and follow the paths shown. The magnetic field strength is B = 0.55 T, and the velocity of the particles is 1200 m/s.
A set of detectors labeled "1" and "2" are positioned at different points along the paths of these particles after they have entered the magnetic field.
**Question:**
Does the particle with the larger charge reach the detector at position "1" or "2"? Explain.
**Diagram Explanation:**
- The image shows a uniform magnetic field directed into the page, represented by "X" marks.
- Two paths are shown with different curvatures indicating the trajectories of the particles as they move through the magnetic field.
- The path leading to detector "1" has a larger radius, while the path leading to detector "2" has a smaller radius.
**Conceptual Explanation:**
The magnetic force exerted on a charged particle moving through a magnetic field causes it to move in a circular path. The radius \( r \) of this path is determined by the formula:
\[
r = \frac{mv}{qB}
\]
where:
- \( m \) is the mass of the particle,
- \( v \) is the speed of the particle,
- \( q \) is the charge of the particle,
- \( B \) is the magnetic field strength.
A particle with a larger charge \( q \) will have a smaller radius of curvature, meaning it will follow a tighter, more curved trajectory.
**Analysis:**
Since the particle with the larger charge has a smaller path radius, it would reach detector "2."
**Additional Calculation:**
If one of the particles is \( \text{Fe}^{3+} \), with a mass of \( 9.277 \times 10^{-23} \) g and charge \( +3e \), calculate the radius of its trajectory.
Convert mass to kilograms:
\[
m = 9.277 \times 10^{-23} \, \text{g} = 9.277 \times 10^{-26} \, \text{kg}
\]
Using charge \( q = 3 \cdot 1.602 \times 10^{-19} \, \text{C} \):
\[
r = \frac{mv](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa91f799b-1b33-41a5-8f4e-af83231854b4%2F27bf706d-7beb-4591-9c1d-4e4accadabda%2Fmfr2n1_processed.png&w=3840&q=75)
Transcribed Image Text:**Magnetic Field Trajectories of Charged Particles**
**Problem Statement:**
Two particles of the same mass enter a magnetic field with the same speed and follow the paths shown. The magnetic field strength is B = 0.55 T, and the velocity of the particles is 1200 m/s.
A set of detectors labeled "1" and "2" are positioned at different points along the paths of these particles after they have entered the magnetic field.
**Question:**
Does the particle with the larger charge reach the detector at position "1" or "2"? Explain.
**Diagram Explanation:**
- The image shows a uniform magnetic field directed into the page, represented by "X" marks.
- Two paths are shown with different curvatures indicating the trajectories of the particles as they move through the magnetic field.
- The path leading to detector "1" has a larger radius, while the path leading to detector "2" has a smaller radius.
**Conceptual Explanation:**
The magnetic force exerted on a charged particle moving through a magnetic field causes it to move in a circular path. The radius \( r \) of this path is determined by the formula:
\[
r = \frac{mv}{qB}
\]
where:
- \( m \) is the mass of the particle,
- \( v \) is the speed of the particle,
- \( q \) is the charge of the particle,
- \( B \) is the magnetic field strength.
A particle with a larger charge \( q \) will have a smaller radius of curvature, meaning it will follow a tighter, more curved trajectory.
**Analysis:**
Since the particle with the larger charge has a smaller path radius, it would reach detector "2."
**Additional Calculation:**
If one of the particles is \( \text{Fe}^{3+} \), with a mass of \( 9.277 \times 10^{-23} \) g and charge \( +3e \), calculate the radius of its trajectory.
Convert mass to kilograms:
\[
m = 9.277 \times 10^{-23} \, \text{g} = 9.277 \times 10^{-26} \, \text{kg}
\]
Using charge \( q = 3 \cdot 1.602 \times 10^{-19} \, \text{C} \):
\[
r = \frac{mv
Transcribed Image Text:**Question: Could the second particle be negatively charged? Explain.**
When analyzing the charge of particles in a system, consider the interactions between them. If the first particle is positively charged, a negatively charged second particle would attract, due to the fundamental principle that opposite charges attract. Observing their behavior in an electric field or their interactions with other charged entities can provide further evidence for their charge state. Consider experimental data or theoretical models to conclude.
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