### Electric Field Calculation from Infinite Sheets of Charge**Problem Statement:**An infinite sheet of charge has a charge density of +25.9 pC/m² and covers the entire x-y plane. A second infinite sheet of charge has a charge density of -58.6 pC/m² and covers the entire y-z plane.**Question:** What is the magnitude of the electric field at any point not on either surface?**Instructions:** Round your answer to 1 decimal place.---When solving this problem, remember that the electric field \( E \) due to an infinite sheet of charge with surface charge density \( \sigma \) is given by:\[ E = \frac{\sigma}{2 \epsilon_0} \]where \( \epsilon_0 \) is the permittivity of free space, \( \epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2/\text{N} \cdot \text{m}^2 \).Since we have two infinite sheets, you need to consider the vector sum of the electric fields produced by each sheet.1. Calculate \( E_1 \) due to the first sheet: \[ E_1 = \frac{+25.9 \times 10^{-12}}{2 \times 8.85 \times 10^{-12}} \, \text{N/C} \]2. Calculate \( E_2 \) due to the second sheet: \[ E_2 = \frac{-58.6 \times 10^{-12}}{2 \times 8.85 \times 10^{-12}} \, \text{N/C} \]3. Since these fields are perpendicular to each other, use the Pythagorean theorem to find the resultant field \( E \): \[ E = \sqrt{E_1^2 + E_2^2} \]Make sure to round the final answer to one decimal place as instructed.

Answered: Image /qna-images/answer/c6404ebb-5ecc-4c88-9b0b-7d39320cfdee.jpg

An infinite sheet charge of has a charge density of +25.9 pC/m-and covers the entire x-y plane. A second infinite sheet of charge ha a charge density of -58.6 pC/m2 covers the entire y-z plane. What is the magnitude of the electric field at any point not on either surface?

An infinite sheet charge of has a charge density of +25.9 pC/m-and covers the entire x-y plane. A second infinite sheet of charge ha a charge density of -58.6 pC/m2 covers the entire y-z plane. What is the magnitude of the electric field at any point not on either surface?

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Concept explainers

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

### Electric Field Calculation from Infinite Sheets of Charge

**Problem Statement:**

An infinite sheet of charge has a charge density of +25.9 pC/m² and covers the entire x-y plane. A second infinite sheet of charge has a charge density of -58.6 pC/m² and covers the entire y-z plane.

**Question:**
What is the magnitude of the electric field at any point not on either surface?

**Instructions:**
Round your answer to 1 decimal place.

---

When solving this problem, remember that the electric field \( E \) due to an infinite sheet of charge with surface charge density \( \sigma \) is given by:
\[ E = \frac{\sigma}{2 \epsilon_0} \]
where \( \epsilon_0 \) is the permittivity of free space, \( \epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2/\text{N} \cdot \text{m}^2 \).

Since we have two infinite sheets, you need to consider the vector sum of the electric fields produced by each sheet.

1. Calculate \( E_1 \) due to the first sheet:
\[
E_1 = \frac{+25.9 \times 10^{-12}}{2 \times 8.85 \times 10^{-12}} \, \text{N/C}
\]

2. Calculate \( E_2 \) due to the second sheet:
\[
E_2 = \frac{-58.6 \times 10^{-12}}{2 \times 8.85 \times 10^{-12}} \, \text{N/C}
\]

3. Since these fields are perpendicular to each other, use the Pythagorean theorem to find the resultant field \( E \):
\[
E = \sqrt{E_1^2 + E_2^2}
\]

Make sure to round the final answer to one decimal place as instructed.

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