### Problem StatementA uniformly charged disk with radius \( R = 40.0 \) cm and uniform charge density \( \sigma = 8.90 \times 10^{-3} \) C/m² lies in the xy-plane, with its center at the origin. What is the electric field (in MN/C) due to the charged disk at the following locations?#### (a) \( z = 5.00 \) cm\[ \boxed{\hspace{3cm}} \text{MN/C} \]#### (b) \( z = 10.0 \) cm\[ \boxed{\hspace{3cm}} \text{MN/C} \]#### (c) \( z = 50.0 \) cm\[ \boxed{\hspace{3cm}} \text{MN/C} \]#### (d) \( z = 200 \) cm\[ \boxed{\hspace{3cm}} \text{MN/C} \]### Explanation for Educational WebsiteThis problem involves calculating the electric field generated by a uniformly charged disk at different points along the z-axis.#### Definitions:- **Radius (R):** The distance from the center of the disk to its edge.- **Uniform charge density (\(\sigma\)):** Charge per unit area on the surface of the disk.- **xy-plane:** A two-dimensional plane determined by the x-axis and y-axis.#### Strategy:Use the formula for the electric field due to a uniformly charged disk at a point along its perpendicular axis (the z-axis):\[ E(z) = \frac{\sigma}{2 \epsilon_0} \left( 1 - \frac{z}{\sqrt{z^2 + R^2}} \right) \]where:- \( z \) is the distance from the disk along the z-axis.- \( \epsilon_0 \) is the permittivity of free space (\( \epsilon_0 \approx 8.85 \times 10^{-12} \text{C}^2/(\text{N} \cdot \text{m}^2) \)).#### Steps:1. **Convert cm to m:** Ensure all distances are in meters for consistency in units.2. **Substitute values into the formula:** Plug in the radius \( R \), charge density \( \sigma \), and distance \( z \)

Hi, as this problem contains multiple sub-parts, hence the first three sub-parts will be solved for…

A uniformly charged disk with radius R = 40.0 cm and uniform charge density = 8.90 x 10-3 C/m² lies in the xy-plane, with its center at the origin. What is the electric field (in MN/C) due to the charged disk at the following locations? (a) z = 5.00 cm MN/C (b) z 10.0 cm MN/C (c) z = 50.0 cm MN/C (d) z = 200 cm MN/C

A uniformly charged disk with radius R = 40.0 cm and uniform charge density = 8.90 x 10-3 C/m² lies in the xy-plane, with its center at the origin. What is the electric field (in MN/C) due to the charged disk at the following locations? (a) z = 5.00 cm MN/C (b) z 10.0 cm MN/C (c) z = 50.0 cm MN/C (d) z = 200 cm MN/C

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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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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

### Problem Statement
A uniformly charged disk with radius \( R = 40.0 \) cm and uniform charge density \( \sigma = 8.90 \times 10^{-3} \) C/m² lies in the xy-plane, with its center at the origin. What is the electric field (in MN/C) due to the charged disk at the following locations?

#### (a) \( z = 5.00 \) cm
\[ \boxed{\hspace{3cm}} \text{MN/C} \]

#### (b) \( z = 10.0 \) cm
\[ \boxed{\hspace{3cm}} \text{MN/C} \]

#### (c) \( z = 50.0 \) cm
\[ \boxed{\hspace{3cm}} \text{MN/C} \]

#### (d) \( z = 200 \) cm
\[ \boxed{\hspace{3cm}} \text{MN/C} \]

### Explanation for Educational Website
This problem involves calculating the electric field generated by a uniformly charged disk at different points along the z-axis.

#### Definitions:
- **Radius (R):** The distance from the center of the disk to its edge.
- **Uniform charge density (\(\sigma\)):** Charge per unit area on the surface of the disk.
- **xy-plane:** A two-dimensional plane determined by the x-axis and y-axis.

#### Strategy:
Use the formula for the electric field due to a uniformly charged disk at a point along its perpendicular axis (the z-axis):

\[ E(z) = \frac{\sigma}{2 \epsilon_0} \left( 1 - \frac{z}{\sqrt{z^2 + R^2}} \right) \]

where:
- \( z \) is the distance from the disk along the z-axis.
- \( \epsilon_0 \) is the permittivity of free space (\( \epsilon_0 \approx 8.85 \times 10^{-12} \text{C}^2/(\text{N} \cdot \text{m}^2) \)).

#### Steps:
1. **Convert cm to m:** Ensure all distances are in meters for consistency in units.
2. **Substitute values into the formula:** Plug in the radius \( R \), charge density \( \sigma \), and distance \( z \)

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