An electron is launched at a 45 ° angle and a speed of 5.0 x 106 m/s from the positive plate of the parallel plate capacitor in the figure show below. The electron lands 4.0 cm away. a. What is the electric field strength inside the capacitor? b. What is the smallest possible spacing between the plates?

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Chapter1: Units, Trigonometry. And Vectors
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**Write-up Criteria**

1. Be neat and organized.
2. Include a drawing of the charge distribution and the point at which the E-field is being evaluated.
3. Include a sample vector diagram, showing the electric-field vectors for critical dq’s.
4. Use the diagrams to help explain any cancellations due to symmetry.
5. Set up the integrals to determine the non-zero electric-field components. Show your work/reasoning for constructing the integrals.
6. Solve the integrals. Box or underline your final solutions.
7. Assess: is your result reasonable? Do the solutions have the correct behavior far away from the charge?

---

**Problem A2:**

An electron is launched at a 45° angle and a speed of \(5.0 \times 10^6 \, \text{m/s}\) from the positive plate of the parallel plate capacitor in the figure shown below. The electron lands 4.0 cm away.

a. What is the electric field strength inside the capacitor?

b. What is the smallest possible spacing between the plates?

**Diagram:**

- A vector \(\vec{v_0}\) indicates the initial velocity of the electron, launched at a 45° angle.
- The trajectory of the electron is represented by a dashed curved line, showing its path.
- The positive plate of the capacitor is marked by a gray rectangle with "+" signs.
- The horizontal distance from the starting point to where the electron lands is labeled as 4.0 cm.
Transcribed Image Text:**Write-up Criteria** 1. Be neat and organized. 2. Include a drawing of the charge distribution and the point at which the E-field is being evaluated. 3. Include a sample vector diagram, showing the electric-field vectors for critical dq’s. 4. Use the diagrams to help explain any cancellations due to symmetry. 5. Set up the integrals to determine the non-zero electric-field components. Show your work/reasoning for constructing the integrals. 6. Solve the integrals. Box or underline your final solutions. 7. Assess: is your result reasonable? Do the solutions have the correct behavior far away from the charge? --- **Problem A2:** An electron is launched at a 45° angle and a speed of \(5.0 \times 10^6 \, \text{m/s}\) from the positive plate of the parallel plate capacitor in the figure shown below. The electron lands 4.0 cm away. a. What is the electric field strength inside the capacitor? b. What is the smallest possible spacing between the plates? **Diagram:** - A vector \(\vec{v_0}\) indicates the initial velocity of the electron, launched at a 45° angle. - The trajectory of the electron is represented by a dashed curved line, showing its path. - The positive plate of the capacitor is marked by a gray rectangle with "+" signs. - The horizontal distance from the starting point to where the electron lands is labeled as 4.0 cm.
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