PH 102 Lecture Notes - Lecture 2: Gravitational Constant, Electric Field, Test Particle

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silvercicada472

3 Nov 2018

School

University of Alabama

Department

Course

PH 102

Professor

Sergio Fabi

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The force between two point charges is given by coulomb"s law: e= kf qq. 2 r q1 and q2 are the charges and r is the distance between the charges. ke is the coulomb constant and is given in the si system by. The si unit for charge is the coulomb (c). The smallest unit of charge is that of the electron or proton. The magnitude of the electronic charge is e. The charge of the proton is qp = e and the charge of the electron is qe = -e. all charges are integral multiples of e. In coulomb"s law f is positive and repulsive if q1 and q2 have the same sign and is negative and attractive if q1 and q2 have the opposite signs. Coulomb"s law is mathematically very similar to the universal law of gravitation between two point masses, which is. 2 r where g is the universal gravitation constant.

Related Questions

Newton’s law of universal gravitation is represented by F = G Mm/ r 2, where F is the gravitational force, M and m are masses, and r is a length. Force has the SI units in kg.m/s^2. What are the SI units of the proportionality constant G?

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Two positivecharges (+Q = 1.00 microcoulombs) are heldin position at +,-2.25 centimeters along the x-axis, as shown in the diagram. A thirdpositive charge (+q = 0.05 microcoulombs and m= 6.5micro-kilograms) is free to move along thex-axis.

The magnitude of force between pairs ofcharges is given by F(Q1,Q2)=kQ1Q2/r^2, where the constant k is8.99x10^9 N*(m^2)/(Coulombs^2), Q1 and Q2 are the electric chargesgiven in Coulombs, and r is the distance between Q1 and Q2 given inmeters. Note that when both forces are positive, the forcebetween them is repulsive.

A)Is the motion of the small charge, q, an example of simple harmonicoscillation? Carefully explain why or why not.

B)Assume q<<Q Find the time for q to complete oneoscillation.

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.

PH 102 Lecture Notes - Lecture 2: Gravitational Constant, Electric Field, Test Particle

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