An infinite plane in the xz plane carries a uniform surface charge density o1 = 74 nc/m2. A second infinite plane carrying a uniform charge density o2 = 38 nC/m2 intersects the xz plane at the z axis and makes an angle of 30° with the xz plane as shown in the figure below. Find the electric field in the xy plane at each of the following locations. + 30° o, (a) x = 6 m, y = 2 m N/C Î + |N/C j (b) x = 6 m, y = 5 m N/C Î + N/C j

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Chapter1: Units, Trigonometry. And Vectors
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**Problem Statement:**

An infinite plane in the xz plane carries a uniform surface charge density \( \sigma_1 = 74 \, \text{nC/m}^2 \). A second infinite plane carrying a uniform charge density \( \sigma_2 = 38 \, \text{nC/m}^2 \) intersects the xz plane at the z-axis and makes an angle of \( 30^\circ \) with the xz plane as shown in the figure below. Find the electric field in the xy plane at each of the following locations.

**Diagram Explanation:**

The diagram displays two intersecting planes:
1. The first plane (in the xz plane) carries a charge density \( \sigma_1 \).
2. The second plane intersects the first plane along the z-axis at an angle of \( 30^\circ \) with the xz plane and has a charge density \( \sigma_2 \).

**Questions:**

(a) For coordinates \( x = 6 \, \text{m}, \, y = 2 \, \text{m} \):
- \( [ \, \, ] \, \text{N/C} \, \hat{i} + [ \, \, ] \, \text{N/C} \, \hat{j} \)

(b) For coordinates \( x = 6 \, \text{m}, \, y = 5 \, \text{m} \):
- \( [ \, \, ] \, \text{N/C} \, \hat{i} + [ \, \, ] \, \text{N/C} \, \hat{j} \)
Transcribed Image Text:**Problem Statement:** An infinite plane in the xz plane carries a uniform surface charge density \( \sigma_1 = 74 \, \text{nC/m}^2 \). A second infinite plane carrying a uniform charge density \( \sigma_2 = 38 \, \text{nC/m}^2 \) intersects the xz plane at the z-axis and makes an angle of \( 30^\circ \) with the xz plane as shown in the figure below. Find the electric field in the xy plane at each of the following locations. **Diagram Explanation:** The diagram displays two intersecting planes: 1. The first plane (in the xz plane) carries a charge density \( \sigma_1 \). 2. The second plane intersects the first plane along the z-axis at an angle of \( 30^\circ \) with the xz plane and has a charge density \( \sigma_2 \). **Questions:** (a) For coordinates \( x = 6 \, \text{m}, \, y = 2 \, \text{m} \): - \( [ \, \, ] \, \text{N/C} \, \hat{i} + [ \, \, ] \, \text{N/C} \, \hat{j} \) (b) For coordinates \( x = 6 \, \text{m}, \, y = 5 \, \text{m} \): - \( [ \, \, ] \, \text{N/C} \, \hat{i} + [ \, \, ] \, \text{N/C} \, \hat{j} \)
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