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.
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.
College Physics
11th Edition
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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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Just need answer please type it. Please put the answer by 2 significant digit
Number: **7.8**
Units: \( \text{C/m}^2 \)
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### 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 \( \sigma \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba35cc5f-959d-4f80-acdd-e9cc0bd31dfa%2F878c5906-0038-4454-848d-cbaa07434cdb%2F5d6ufc2_processed.jpeg&w=3840&q=75)
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.
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 \( \sigma \).
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