1.1 Theoretical CalculationsConsider a simple electroscope consisting of two insulating, massless strings of length \( L \) with small point-masses (\( m \)) firmly attached at one end (see Fig. 1). Assuming the point-masses hold equal charge \( Q \), show that the magnitude of the Coulomb force \( F \) between the two point-masses is given by:\[F = \frac{kQ^2}{r^2} = mg \cdot \tan(\theta),\]where \( r = D + 2L \cdot \sin(\theta) \) (show this!) is the separation distance between the two point-masses, and \( \theta \) is the angle each massless string makes with respect to the vertical. **Figure 1: Electroscope Schematic**This schematic illustrates an electroscope, featuring two small point-masses \( m \) capable of carrying charge. Each mass is suspended by a massless string of length \( L \), allowing it to pivot around a fixed mounting point. The setup is designed with two pivot points positioned at a distance \( D \) apart.Diagram Explanation:- Two red circles labeled \( m \) represent the point-masses capable of carrying charge.- Each mass is connected to a string of length \( L \).- The strings originate from fixed points mounted above the masses.- The masses hang at an angle \( \theta \) from the vertical, separating the two masses horizontally by a distance \( r \).- The pivot points are separated by a horizontal distance \( D \).- The strings and the distance \( r \) are indicated by black lines and arrows, while the angles and distances are marked for clarity.This diagram helps visualize the interaction of charges on the masses and demonstrates fundamental principles of electrostatics and mechanics.

Answered: Image /qna-images/answer/2b1924d3-f6bf-44dd-86de-6000453e8a0f.jpg

Consider a simple electroscope consisting of two insulating, massless strings of length L with small point-masses (m) firmly attached at one end (see Fig. 1). Assuming the point-masses hold equal charge Q, show that the magnitude of the Coulomb force F between the two point-masses is given by: (2) Q² F = k 2 where r = D+2L sin(0) (show this!) is the separation distance between the two point-masses, and = mg.tan(0),

Consider a simple electroscope consisting of two insulating, massless strings of length L with small point-masses (m) firmly attached at one end (see Fig. 1). Assuming the point-masses hold equal charge Q, show that the magnitude of the Coulomb force F between the two point-masses is given by: (2) Q² F = k 2 where r = D+2L sin(0) (show this!) is the separation distance between the two point-masses, and = mg.tan(0),

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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Question

1.1 Theoretical Calculations

Consider a simple electroscope consisting of two insulating, massless strings of length \( L \) with small point-masses (\( m \)) firmly attached at one end (see Fig. 1). Assuming the point-masses hold equal charge \( Q \), show that the magnitude of the Coulomb force \( F \) between the two point-masses is given by:

\[
F = \frac{kQ^2}{r^2} = mg \cdot \tan(\theta),
\]

where \( r = D + 2L \cdot \sin(\theta) \) (show this!) is the separation distance between the two point-masses, and \( \theta \) is the angle each massless string makes with respect to the vertical.

**Figure 1: Electroscope Schematic**

This schematic illustrates an electroscope, featuring two small point-masses \( m \) capable of carrying charge. Each mass is suspended by a massless string of length \( L \), allowing it to pivot around a fixed mounting point. The setup is designed with two pivot points positioned at a distance \( D \) apart.

Diagram Explanation:
- Two red circles labeled \( m \) represent the point-masses capable of carrying charge.
- Each mass is connected to a string of length \( L \).
- The strings originate from fixed points mounted above the masses.
- The masses hang at an angle \( \theta \) from the vertical, separating the two masses horizontally by a distance \( r \).
- The pivot points are separated by a horizontal distance \( D \).
- The strings and the distance \( r \) are indicated by black lines and arrows, while the angles and distances are marked for clarity.

This diagram helps visualize the interaction of charges on the masses and demonstrates fundamental principles of electrostatics and mechanics.

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