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)...

See similar textbooks

Similar questions

What would the final speed be (infinitely far away) of a charge of +q and mass, m, if released at rest from the edge of a fixed , uniformly charged disk of radius a and total charge Q? The thickness of the disk is irrelevant.
Two identical particles, each having charge +q, are fixed in space and separated by a distance d. A third particle with charge −Q is free to move and lies initially at rest on the perpendicular bisector of the two fixed charges a distance x from the midpoint between those charges (Fig.). (a) Show that if x is small compared with d, the motion of −Q is simple harmonic along the perpendicular bisector. (b) Determine the period of that motion. (c) Howfast will the charge −Q be moving when it is at the midpoint between the two fixed charges if initially it is released at a distance a << d from the midpoint?
Electrostatic field at point A (10, -2,0) in empty space Observed as E = 2keux Determine the location (xs, ys, zs) of the point Q = -2 [C] that is likely to form this area. It shows the constant ke = 1 / (4πε). Write the numerical value of the sum of the coordinate points xs + ys + zs as an answer.
I need the answer as soon as possible
[Numbers change] In the early 1900's Robert Millikan discovered the peculiar property that charge came in little packets, no smaller than e = 1.602 x 10-19 C -- he had measured the charge of the electron. Here's (roughly) how he did it. He removed an electron from an initially neutral droplet of oil with diameter 0.8 um. In a vacuum, he positioned the droplet between two metallic plates separated by 4 mm and fiddled with the potential (voltage) across the plates until the droplet would hover against the force of gravity. Droplets of this size with +e charge would hover, but only for a particular voltage (otherwise they would sink or rise). Given the parameters stated here, and the fact that the density of the oil was 815 kg/m³, what was the voltage that made the droplets hover? (give your answer with 0.1 V precision)
Assume that you are way out in space, very very far away from other masses, and you have two identical particleseach of which has the charge of an electron. Suppose you hold both of these particles 0.1m apart from each other and then release them. What mass would these particles have to have in order for the gravitational force to exactly balance the electric force? (So that they don't move.) [Put units on all numbers.]
Two metallic sphere of radius 1 cm and 3 cm respectively are separated by a large distance D,(D»lcm). Initially, the smaller sphere carries a charge Q while the larger one is uncharged. If a thin metallic wire is connected between the two spheres, the ratio of the charges on the smaller sphere to the larger on in equilib- rium will be : [IISc. 2012] (a) 1/3 (b) 1/9 (c) 3 (d) 9
(a) Find the electrostatic field at a distance of 5 cm from a 2µC charge. (b) What is the magnitude and direction of the force on a proton placed at this point? [ [Given Data , Coulomb constant ke= 8.99x10° Nm?/C?] el KSJ A postal employee drives a delivery truck along the route shown in fig. Use component method to determine the magnitude and direction of the truck's resultant displacement. STOP 3.1 km 4.0 km 45° START 2.6 km
QUESTION 11 Redo Example 18.1 (p. 773, "How strong is the Coulomb force relative to the gravitational force?") for two electrons situated 53 pm apart. Express your answer asnx 1042 and type in just the value of n with two significant figures.
Two point charges of mass m each are suspended in the gravitational field of the Earth by two non-conducting massless strings, each of length 1, attached to the same fixed point. The spheres are given equal charges Q of the same sign. As a result each string makes angle a to the vertical (see figure below). Calculate m, if 1 = 78.3 cm, Q = 4 µC and a = π/6. Take Coulomb constant ke-8.99×109 Nm² C-2. Give your answer in grams. / / / / L d M
Two point charges of mass m each are suspended in the gravitational field of the Earth by two non-conducting massless strings, each of length 7, attached to the same fixed point. The spheres are given equal charges Q of the same sign. As a result each string makes angle a to the vertical (see figure below). Calculate m, if I = 82.1 cm, Q = 4 µC and a = /6. Take Coulomb constant k = 8.99x109 N m² C-2. Give your answer in grams. 11 // e M 7 /// C d e M
Two identical particles, each having charge +q, are fixed in space and separated by a distance d. A third particle with charge -Q is free to move and lies initially at rest on the perpendicular bisector of the two fixed charges a distance x from the midpoint between those charges (as shown). (a) Show that if x is small compared with d, the motion of -Q is simple harmonic along the perpendicular bisector. (b) Determine the period of that motion. (c) How fast will the charge -Q be moving when it is at the midpoint between the two fixed charges if initially it is released at a distance a << d from the midpoint?