2) тог a) Find Ex and Ey at pourt where the rod has CA total charge Q. Assous a uniform charge density. X=10cm. az 10 Q=107% b) Find the acceleration on an electron placed at p

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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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### Problem Description

We have a rod with length \( a \) and total charge \( Q \). The problem involves the following tasks:

1. **Determine the Electric Field \( E_x \) and \( E_y \) at Point \( P \):**

   - \( P \) is located at a distance \( x \) from the nearest end of the rod.
   - Assume the rod has a uniform charge density.

2. **Find the Acceleration of an Electron Placed at \( P \):**

   - Given:
     - \( x = 10 \, \text{cm} \)
     - \( a = 10 \, \text{cm} \)
     - \( Q = 16 \times 10^{-9} \, \text{C} \)

### Diagram Explanation

The diagram illustrates:

- A horizontal line representing the rod, with length \( a \).
- A point \( P \) located at a perpendicular distance \( x \) from the rod's nearest end.
- \( E_x \) and \( E_y \) represent the components of the electric field at point \( P \).

### Solution Steps

To solve this problem, one would typically:

1. **Calculate the Electric Field:**
   - Use integration to determine \( E_x \) and \( E_y \) by considering contributions from each infinitesimal charge element along the rod.

2. **Determine Electron Acceleration:**
   - Use the calculated electric field to find the force on an electron at point \( P \), and apply \( F = ma \) to find the acceleration.

This problem involves concepts of electrostatics and requires knowledge of integrating electric fields from continuous charge distributions.
Transcribed Image Text:### Problem Description We have a rod with length \( a \) and total charge \( Q \). The problem involves the following tasks: 1. **Determine the Electric Field \( E_x \) and \( E_y \) at Point \( P \):** - \( P \) is located at a distance \( x \) from the nearest end of the rod. - Assume the rod has a uniform charge density. 2. **Find the Acceleration of an Electron Placed at \( P \):** - Given: - \( x = 10 \, \text{cm} \) - \( a = 10 \, \text{cm} \) - \( Q = 16 \times 10^{-9} \, \text{C} \) ### Diagram Explanation The diagram illustrates: - A horizontal line representing the rod, with length \( a \). - A point \( P \) located at a perpendicular distance \( x \) from the rod's nearest end. - \( E_x \) and \( E_y \) represent the components of the electric field at point \( P \). ### Solution Steps To solve this problem, one would typically: 1. **Calculate the Electric Field:** - Use integration to determine \( E_x \) and \( E_y \) by considering contributions from each infinitesimal charge element along the rod. 2. **Determine Electron Acceleration:** - Use the calculated electric field to find the force on an electron at point \( P \), and apply \( F = ma \) to find the acceleration. This problem involves concepts of electrostatics and requires knowledge of integrating electric fields from continuous charge distributions.
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