Three point charges are positioned as follows: a positive charge +q = +lql is located on the x-axis at the point (b, 0) = position (1) (note: b = +lbl), a negative charge -2q = -l2ql is located on the x-axis at the point (-2b, 0) = position (2), and the third, a positive point charge +q/3 = +lq/3l is located at the point (-2/3b, -1/3b) = position (3). What is the symbolic expression for the electric field at the origin due to this system of point charges, in terms of ke, q and b and what is the magnitude of the electric field at the origin? To answer this question, please go through the following steps: **Electric Field and Point Charges: An Educational Guide**Three point charges are positioned as follows: - A positive charge \( +q = +|q| \) is located on the x-axis at the point \( (b, 0) = \text{position} (1) \) where \( b = +|b| \).- A negative charge \( -2q = -|2q| \) is located on the x-axis at the point \( (-2b, 0) = \text{position} (2) \).- The third charge, a positive point charge \( +q/3 = +|q/3| \), is located at the point \( \left( -\frac{2b}{3}, -\frac{1b}{3} \right) = \text{position} (3) \).**Objective:** Determine the symbolic expression for the electric field at the origin due to this system of point charges, considering \( k_e, q, \) and \( b \).---**Instructions:**1. **Draw Electric Field Vectors:** Draw the three electric field vectors originating from the origin that contribute to the net electric field from each of the three source charges.2. **Understanding Components:** Determine the x and y-components of these vectors.**Steps:****(A)** What is the electric field at the origin due to only the \( +q \) charge at position 1? \[ \vec{E_1} = q \hat{i} + 0 \hat{j} \]**(B)** What is the electric field at the origin due to both the \( +q \) charge at position (1) and the \( -2q \) charge at position (2)? \[ \vec{E_{1+2}} = 0 \hat{i} + 0 \hat{j} \]**(C)** What is the electric field at the origin due to only the \( +q/3 \) charge at position (3)? Factor out unknowns and enter numerically with four significant figures. \[ \vec{E_3} = \frac{3k_eq}{b^2} \left( 0 \hat{i} + 0 \hat{j} \right) \]**(D)** What is the symbolic expression for the electric field at the origin due to the system

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College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Three point charges are positioned as follows: a positive charge +q = +lql is located on the x-axis at the point (b, 0) = position (1) (note: b = +lbl), a negative charge -2q = -l2ql is located on the x-axis at the point (-2b, 0) = position (2), and the third, a positive point charge +q/3 = +lq/3l is located at the point (-2/3b, -1/3b) = position (3). What is the symbolic expression for the electric field at the origin due to this system of point charges, in terms of k_e, q and b and what is the magnitude of the electric field at the origin? To answer this question, please go through the following steps:

**Electric Field and Point Charges: An Educational Guide**

Three point charges are positioned as follows:

- A positive charge \( +q = +|q| \) is located on the x-axis at the point \( (b, 0) = \text{position} (1) \) where \( b = +|b| \).
- A negative charge \( -2q = -|2q| \) is located on the x-axis at the point \( (-2b, 0) = \text{position} (2) \).
- The third charge, a positive point charge \( +q/3 = +|q/3| \), is located at the point \( \left( -\frac{2b}{3}, -\frac{1b}{3} \right) = \text{position} (3) \).

**Objective:** Determine the symbolic expression for the electric field at the origin due to this system of point charges, considering \( k_e, q, \) and \( b \).

---

**Instructions:**

1. **Draw Electric Field Vectors:** Draw the three electric field vectors originating from the origin that contribute to the net electric field from each of the three source charges.

2. **Understanding Components:** Determine the x and y-components of these vectors.

**Steps:**

**(A)** What is the electric field at the origin due to only the \( +q \) charge at position 1?
\[ \vec{E_1} = q \hat{i} + 0 \hat{j} \]

**(B)** What is the electric field at the origin due to both the \( +q \) charge at position (1) and the \( -2q \) charge at position (2)?
\[ \vec{E_{1+2}} = 0 \hat{i} + 0 \hat{j} \]

**(C)** What is the electric field at the origin due to only the \( +q/3 \) charge at position (3)? Factor out unknowns and enter numerically with four significant figures.
\[ \vec{E_3} = \frac{3k_eq}{b^2} \left( 0 \hat{i} + 0 \hat{j} \right) \]

**(D)** What is the symbolic expression for the electric field at the origin due to the system

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