II Review A 10.7 µC particle with a mass of 2.90x10-5 kg moves perpendicular to a 0.930 T magnetic field in a circular path of radius 27.5 m. Part A For the steps and strategies involved in solving a similar problem, you may view the following Quick Example 22-8 video: How fast is the particle moving? Express your answer in meters per second. REASONING AND SOLUTION . Cakulate the time Treguired for a partide of mass m and charge q to complete a circular orbit in a magnecic field of strength & ? For any obiect in uniform circular motion m/s For a charged object moving in a uniform magnetic field Submit Request Answer Part B How long will it take the particle to complete one orbit? Express your answer in seconds. ? t = S Submit Request Answer

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### Educational Resource: Particle Motion in a Magnetic Field

**Problem Statement:**
A 10.7 μC particle with a mass of \(2.90 \times 10^{-5}\) kg moves perpendicularly to a 0.930 T magnetic field in a circular path of radius 27.5 m.

For the steps and strategies involved in solving a similar problem, you may view the following [Quick Example 22-8](#) video.

**REASONING AND SOLUTION:**

- **Objective:**
  - Calculate the time \( T \) required for a particle of mass \( m \) and charge \( q \) to complete a circular orbit in a magnetic field of strength \( B \).

- **Formulas:**
  - For any object in uniform circular motion:
    \[
    v = \frac{2 \pi r}{T}
    \]
  - For a charged object moving in a uniform magnetic field:
    \[
    r = \frac{mv}{qB}
    \]

**Diagram Description:**
- A circle is shown with arrows indicating the magnetic field direction and the particle's path. The circle's center is marked, and radial lines are drawn, signifying uniform circular motion.

### Questions for Consideration

**Part A:**
- **Question:** How fast is the particle moving?
  - **Answer Format:** Express your answer in meters per second.
  - **Input Box:** 
    \[
    v = \quad \text{m/s}
    \]
  - **Submit Button**: Click to submit your answer.
  - **Request Answer:** Option to request the solution.

**Part B:**
- **Question:** How long will it take the particle to complete one orbit?
  - **Answer Format:** Express your answer in seconds.
  - **Input Box:**
    \[
    t = \quad \text{s}
    \]
  - **Submit Button:** Click to submit your answer.
  - **Request Answer:** Option to request the solution.

Review the video and apply the formulas to solve the questions, deepening your understanding of particle motion in magnetic fields.
Transcribed Image Text:### Educational Resource: Particle Motion in a Magnetic Field **Problem Statement:** A 10.7 μC particle with a mass of \(2.90 \times 10^{-5}\) kg moves perpendicularly to a 0.930 T magnetic field in a circular path of radius 27.5 m. For the steps and strategies involved in solving a similar problem, you may view the following [Quick Example 22-8](#) video. **REASONING AND SOLUTION:** - **Objective:** - Calculate the time \( T \) required for a particle of mass \( m \) and charge \( q \) to complete a circular orbit in a magnetic field of strength \( B \). - **Formulas:** - For any object in uniform circular motion: \[ v = \frac{2 \pi r}{T} \] - For a charged object moving in a uniform magnetic field: \[ r = \frac{mv}{qB} \] **Diagram Description:** - A circle is shown with arrows indicating the magnetic field direction and the particle's path. The circle's center is marked, and radial lines are drawn, signifying uniform circular motion. ### Questions for Consideration **Part A:** - **Question:** How fast is the particle moving? - **Answer Format:** Express your answer in meters per second. - **Input Box:** \[ v = \quad \text{m/s} \] - **Submit Button**: Click to submit your answer. - **Request Answer:** Option to request the solution. **Part B:** - **Question:** How long will it take the particle to complete one orbit? - **Answer Format:** Express your answer in seconds. - **Input Box:** \[ t = \quad \text{s} \] - **Submit Button:** Click to submit your answer. - **Request Answer:** Option to request the solution. Review the video and apply the formulas to solve the questions, deepening your understanding of particle motion in magnetic fields.
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