2) → x Figure 2: Semi-circular line of charge, with radius r. Consider the charge configuration in Figure 2. The semi-circular line of charge has a radius r, and linear charge density A = B sin (0). What is the electric field at point p? Note: Express your answer in rectangular coordinates.

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**Title: Understanding a Semi-Circular Line of Charge**

**Figure 2: Semi-Circular Line of Charge, with Radius \( r \)**

**Description:**
This figure illustrates a semi-circular line of charge with a radius \( r \). In the diagram, a semi-circle is centered at a point \( p \). The angle \( \theta \) is measured from the horizontal \( x \)-axis to the radius \( r \).

**Scenario:**
Consider the charge configuration shown in Figure 2. The semi-circular line of charge has a constant radius \( r \) and a linear charge density given by \( \lambda = \beta \sin(\theta) \), where \( \beta \) is a constant.

**Objective:**
Determine the electric field at point \( p \).

**Instructions:**
Calculate the electric field at point \( p \) due to the given charge distribution. Express your answer in rectangular coordinates (i.e., in terms of \( x \) and \( y \) components).
Transcribed Image Text:**Title: Understanding a Semi-Circular Line of Charge** **Figure 2: Semi-Circular Line of Charge, with Radius \( r \)** **Description:** This figure illustrates a semi-circular line of charge with a radius \( r \). In the diagram, a semi-circle is centered at a point \( p \). The angle \( \theta \) is measured from the horizontal \( x \)-axis to the radius \( r \). **Scenario:** Consider the charge configuration shown in Figure 2. The semi-circular line of charge has a constant radius \( r \) and a linear charge density given by \( \lambda = \beta \sin(\theta) \), where \( \beta \) is a constant. **Objective:** Determine the electric field at point \( p \). **Instructions:** Calculate the electric field at point \( p \) due to the given charge distribution. Express your answer in rectangular coordinates (i.e., in terms of \( x \) and \( y \) components).
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