In the figure a small, nonconducting ball of mass m = 1.5 mg and charge q = 2.9 x 108 C (distributed uniformly through its volume) hangs from an insulating thread that makes an angle 0 = 41° with a vertical, uniformly charged nonconducting sheet (shown in cross section). Considering the gravitational force on the ball and assuming the sheet extends far vertically and into and out of the page, calculate the surface charge density o of the sheet.

University Physics Volume 2
18th Edition
ISBN:9781938168161
Author:OpenStax
Publisher:OpenStax
Chapter7: Electric Potential
Section: Chapter Questions
Problem 70P: A simple and common technique for accelerating electrons is shown in Figure 7.46, where there is a...
icon
Related questions
Question

Just need answer please type it. Please put the answer by 2 significant digit 

---

**Your answer is partially correct.**

In the figure, a small, nonconducting ball of mass \( m = 1.5 \, \text{mg} \) and charge \( q = 2.9 \times 10^{-8} \, \text{C} \) (distributed uniformly through its volume) hangs from an insulating thread that makes an angle \( \theta = 41^\circ \) with a vertical, uniformly charged nonconducting sheet (shown in cross section). Considering the gravitational force on the ball and assuming the sheet extends far vertically and into and out of the page, calculate the surface charge density \( \sigma \) of the sheet.

![Physics diagram illustrating a hanging charged ball](https://user-images.githubusercontent.com/random_image_url)

Number: **7.8**
Units: \( \text{C/m}^2 \)

---

### Diagram Explanation:

The diagram associated with the problem shows:
- A vertical, uniformly charged nonconducting sheet depicted as a green solid line.
- The sheet extends vertically and into and out of the page. 
- An insulating thread is attached to a small, nonconducting ball.
- The thread forms an angle \( \theta = 41^\circ \) with the vertical line representing the sheet.
- The ball has a given mass \( m = 1.5 \, \text{mg} \) and charge \( q = 2.9 \times 10^{-8} \, \text{C} \).
- The forces acting on the ball would include the gravitational force pointing downward and the electrostatic force due to the charged sheet.

This scenario sets up a physics problem where we need to balance the forces acting on the ball to find the surface charge density \( \sigma \) of the sheet that maintains the ball in equilibrium at the given angle.

For any further calculations, students usually need to apply principles from electrostatics and mechanics such as Coulomb's Law, the definition of surface charge density, and trigonometric relationships to solve for \( \sigma \).
Transcribed Image Text:--- **Your answer is partially correct.** In the figure, a small, nonconducting ball of mass \( m = 1.5 \, \text{mg} \) and charge \( q = 2.9 \times 10^{-8} \, \text{C} \) (distributed uniformly through its volume) hangs from an insulating thread that makes an angle \( \theta = 41^\circ \) with a vertical, uniformly charged nonconducting sheet (shown in cross section). Considering the gravitational force on the ball and assuming the sheet extends far vertically and into and out of the page, calculate the surface charge density \( \sigma \) of the sheet. ![Physics diagram illustrating a hanging charged ball](https://user-images.githubusercontent.com/random_image_url) Number: **7.8** Units: \( \text{C/m}^2 \) --- ### Diagram Explanation: The diagram associated with the problem shows: - A vertical, uniformly charged nonconducting sheet depicted as a green solid line. - The sheet extends vertically and into and out of the page. - An insulating thread is attached to a small, nonconducting ball. - The thread forms an angle \( \theta = 41^\circ \) with the vertical line representing the sheet. - The ball has a given mass \( m = 1.5 \, \text{mg} \) and charge \( q = 2.9 \times 10^{-8} \, \text{C} \). - The forces acting on the ball would include the gravitational force pointing downward and the electrostatic force due to the charged sheet. This scenario sets up a physics problem where we need to balance the forces acting on the ball to find the surface charge density \( \sigma \) of the sheet that maintains the ball in equilibrium at the given angle. For any further calculations, students usually need to apply principles from electrostatics and mechanics such as Coulomb's Law, the definition of surface charge density, and trigonometric relationships to solve for \( \sigma \).
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Unit conversion
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
University Physics Volume 2
University Physics Volume 2
Physics
ISBN:
9781938168161
Author:
OpenStax
Publisher:
OpenStax
Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
Physics
ISBN:
9781133104261
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Physics for Scientists and Engineers with Modern …
Physics for Scientists and Engineers with Modern …
Physics
ISBN:
9781337553292
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Physics for Scientists and Engineers: Foundations…
Physics for Scientists and Engineers: Foundations…
Physics
ISBN:
9781133939146
Author:
Katz, Debora M.
Publisher:
Cengage Learning
Physics for Scientists and Engineers, Technology …
Physics for Scientists and Engineers, Technology …
Physics
ISBN:
9781305116399
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning