8. * Coulomb's Law described the force of attraction between charged particles. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The figure shows particles with charge +1 located at positions 0 and 2 on a coordinate line and a particle with charge -1 at a position x between them. It follows from Coulomb's Law that the net force acting on the middle particle is k F(x)==+₂₁² [0

8. * Coulomb's Law described the force of attraction between charged particles. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. The figure shows particles with charge +1 located at positions 0 and 2 on a coordinate line and a particle with charge -1 at a position x between them. It follows from Coulomb's Law that the net force acting on the middle particle is k F(x)==+₂₁² [0

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter20: Electric Potential And Capacitance

Section: Chapter Questions

Problem 18P

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Construct Your Own Problem Consider identical spherical conducting space ships in deep space where gravitational fields from other bodies are negligible compared to the gravitational attraction between the ships. Construct a problem in which you place identical excess charges on the space ships to exactly counter their gravitational attraction. Calculate the amount of excess charge needed. Examine whether that charge depends on the distance between the centers of the ships, the masses of the ships, or any other factors. Discuss whether this would be an easy, difficult, or even impossible thing to do in practice.
Compare and contrast the Coulomb force field and the electric field. To do this, make a list of five properties for the Coulomb force field analogous to the five properties listed for electric field lines. Compare each item in your list of Coulomb force field properties with those of the electric field—are they the same or different? (For example, electric field lines cannot cross. Is the same true for Coulomb field lines?)
(a) Common transparent tape becomes charged when pulled from a dispenser. If one piece is placed above another, the repulsive force can be great enough to support the top piece’s weight. Assuming equal point charges (only an approximation), calculate the magnitude of the charge if electrostatic force is great enough to support the weight of a mg piece of tape held 1.00 cm above another. (b) Discuss whether the magnitude of this charge is consistent with what is typical of static electricity.
A large charge +Q and a small charge q are a short distance apart. How do the electric forces on each charge compare? Is this comparison described by another physical law? (Hint: See Chapter 3.4.)
A simple and common technique for accelerating electrons is shown in Figure 18.55, where there is a uniform electric field between two plates. Electrons are released, usually from a hot filament, near the negative plate, and there is a small hole in the positive plate that allows the electrons to continue moving. (a) Calculate the acceleration of the electorn if the field strength is 2.50104 N/C. (b) Explain why the electron will not be pulled back to the positive plate once it moves through the hole.
An object with negative charge is placed in a region of space where the electric field is directed vertically upward. What is the direction of the electric force exerted on this charge? (a) It is up. (b) It is down. (c) There is no force. (d) The force can be in any direction.
Review. From a large distance away, a particle of mass m1, and positive charge q1 is fired at speed in the positive x direction straight toward a second particle, originally stationary but free to move, with mass m2, and positive charge q2. Both particles are constrained to move only along the x axis. (a) At the instant of closest approach, both particles will be moving at the same velocity. Find this velocity, (b) Find the distance of closest approach. After the interaction, the particles will move far apart again. At this time, find the velocity of (c) the particle of mass m1, and (d) the particle of mass m2.
Integrated Concepts Figure 18.57 shows an electron passing between two charged metal plates that create an 100 N/C vertical electric field perpendicular to the electron's original horizontal velocity. (These can be used to change the electron’s direction, such as in an oscilloscope.) The initial speed of the electron is 3.00106 m/s, and the horizontal distance it travels in the uniform field is 4.00 cm. (a) What is its vertical deflection? (b) What is the vertical component of its final velocity? (c) At what angle does it exit? Neglect any edge effects.
Why does a car always attract dust right after it is polished? (Note that car wax and car tires are insulators.)
Rocket observations show that dust particles in Earths upper atmosphere are often electrically charged. (a) Find the distance separating two dust particles if each has a charge of +e and the Coulomb force between them has magnitude 1.00 1014 N. (b) Calculate the mass of one of the dust panicles if this Coulomb force would accelerate it at 4.50 108 m/s2. (In the upper atmosphere, effects from other nearby charges typically result in a small net force and acceleration.)
Integrated Concepts An electron has an initial velocity of 5.00106m/s in a uniform 2.00105N/C strength electric field. the field accelerates the electron in the direction opposite to its initial velocity. (a) What is the direction of the electric field? (b) How far does the electron travel before coming to rest? (c) How long does it take the electron to come to rest? (d) What is the electron’s velocity when it returns to its starting point?
Review. A molecule of DNA (deoxyribonucleic acid) is 2.17m long. The ends of the molecule become singly ionized: negative on one end, positive on the other. The helical molecule acts like a spring and compresses 1.00% upon becoming charged. Determine the effective spring constant of the molecule.