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Physics 1029A/B Study Guide - Final Guide: Stationary Point, Physical Constant, Potential Energy

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School
Western University
Department
Physics
Course
Physics 1029A/B
Professor
Martin Zinke- Allmang

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Document Summary

Coulomb"s law: relation between electric force and charge, magnitude of electric force between two charged spheres is proportional to the absolute amount of charge on each sphere and is proportional to. 1/r2 where r is the distance between two spheres. O: physical constant, permittivity of vacuum, 8. 85x10-12 c2/(nm2) Two equal point charges of 1c each, placed at a distance of 1 m, attract each other with a force of 9 x 109 nm2/c2. Elementary charge: smallest amount of charge for electrons, 1. 6 x 10-19c. If charges have the same sign f is positive. If charges have opposite signs f is negative. At every position within an arrangement of stationary charges, the stationary electric field is the force vector that acts on a mobile point charge of unit charge if placed at that position. Defines magnitude of electric field due to a simple stationary point charge. The field varies with distance from the stationary point charge as 1/r2.

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Related Questions

Two-point charges attract each other with an electric force of magnitude F. If the charge on one of the particles is reduced to one-third its original value and the distance between the particles is doubled, what is the resulting magnitude of the electric force between them?
(a)F/12 F(b) 3F(c) 6F(d) 1F (e) 4 F 

 

Consider two conducting spheres with radii and  separated by a distance much greater than either radius. A total charge Q is shared between the spheres. We wish to show that when the electric potential energy of the system has a minimum value, the potential difference between the spheres is zero. The total charge Q is equal to , where represents the charge on the first sphere and the charge on the second. Because the spheres are very far apart, you can assume the charge of each is uniformly distributed over its surface.

(a) Show that the energy associated with a single conducting sphere of radius R and charge q surrounded by a vacuum is .

(b) Find the total energy of the system of two spheres in terms of , total charge Q and the radii  and .

(c) To minimize the energy, differentiate the result to part (b) with respect to and set the derivative equal to zero. Solve for in terms of Q and the radii.

(d) From the result to part (c), find the charge .

(e) Find the potential of each sphere.

(f) What is the potential difference between the spheres?

Two small identical conducting spheres are separated by a distanceL horizontally that is much larger than their radii. The leftmostof the two spheres experiences a force F directed to the right dueto the presence of the second sphere. The two spheres are broughtinto contact and 5x10^12 electrons are transferred from one sphereto the other (the charge of an electron is 1.6x10^-19 Coulombs).The spheres are then separated by a distance L again and theleftmost sphere experiences a force of magnitude 4/5 F.

A) Describe the initial charge of the two spheres. Explain yourreasoning

B) What is the direction of the force on the leftmost sphere afterthe objects have been in contact? Explain.

C) Write an expression relating the magnitude of the force beforethe spheres touch to that after they touch.


D) Imagine that the two charged objects had charges of Q1 and Q2.When they are touched they transfer an amount of charge ?Q. Writean expression involving Q1and Q2 (total, two expressions) in termsof the total charge of the system(1) and the amount of chargetransferred (2).

E) Using the expression for E, find equations for Q1and Q2 in termsof the total charge and ?Q

F) Find the initial charge on each of the spheres before they weretouched.