78418691-mp-em-ass-1-coulomb-s-law.pdf 1o1x65

Assignment 1: Coulomb's Law Due: 8:00am on Wednesday, January 11, 2012 Note: To understand how points are awarded, read your instructor's Grading Policy. [Switch to Standard Assignment View]

Coulomb's Law Tutorial Learning Goal: To understand how to calculate forces between charged particles, particularly the dependence on the sign of the charges and the distance between them. Coulomb's law describes the force that two charged particles exert on each other (by Newton's third law, those two forces must be equal and opposite). The force exerted by particle 2 (with charge ) on particle 1 (with charge ) is proportional to the charge of each particle and inversely proportional to the square of the distance between them:

,

where

and

is the unit vector pointing from particle 2 to particle 1. The force vector will be parallel or

antiparallel to the direction of , parallel if the product and antiparallel if if the charges are of opposite sign and repulsive if the charges are of the same sign.

; the force is attractive

Part A

Consider two positively charged particles, one of charge (particle 0) fixed at the origin, and another of charge force

on particle 0 due to particle 1?

Express your answer (a vector) using any or all of , ANSWER: = Part B

(particle 1) fixed on the y-axis at

Correct

,

,

, , , and .

. What is the net

Now add a third, negatively charged, particle, whose charge is (particle 2). Particle 2 fixed on the y-axis at position particle 1 and particle 2? Express your answer (a vector) using any or all of , ANSWER: =

,

. What is the new net force on particle 0, from ,

,

,

, , , and .

Correct

Part C Particle 0 experiences a repulsion from particle 1 and an attraction toward particle 2. For certain values of , the repulsion and attraction should balance each other, resulting in no net force. For what ratio no net force on particle 0? Express your answer in of any or all of the following variables: , ANSWER:

,

,

and

is there

.

= Correct Part D

Now add a fourth charged particle, particle 3, with positive charge , fixed in the yz-plane at . What is the net force Hint D.1 Find the magnitude of force from particle 3

on particle 0 due solely to this charge?

Hint not displayed Hint D.2 Vector components Hint not displayed Express your answer (a vector) using , ANSWER: = Correct

,

,

, , , and . Include only the force caused by particle 3.

Exercise 21.4 You have a pure (24-karat) gold ring with mass number of Part A

. Gold has an atomic mass of

and an atomic

.

How many protons are in the ring? ANSWER: 4.27×1024 = Correct Part B What is their total positive charge? ANSWER: 6.83×105 = Correct Part C If the ring carries no net charge, how many electrons are in it? ANSWER: 4.27×1024 = Correct

Exercise 21.22 Two point charges are placed on the x-axis as follows: charge = 5.00 Part A

is at

-0.296

= 4.05

is located at

0.197

, and charge

.

What is the magnitude of the total force exerted by these two charges on a negative point charge that is placed at the origin? ANSWER: 2.55×10−6 = Correct

= -6.00

Part B What is the direction of the total force exerted by these two charges on a negative point charge is placed at the origin? ANSWER: to the + direction to the - direction perpendicular to the -axis the force is zero

= -6.00

that

Correct

Problem 21.66 A charge 4.97 positive x-axis at = 3.01 . Part A

is placed at the origin of an xy-coordinate system, and a charge -1.99 = 3.98

. A third particle, of charge 6.05

is placed on the

is now placed at the point

= 3.98

,

Find the x-component of the total force exerted on the third charge by the other two. ANSWER: 8.66×10−5 = Correct Part B Find the y-component of the total force exerted on the third charge by the other two. ANSWER: −5.40×10−5 = Correct Part C Find the magnitude of the total force acting on the third charge. ANSWER: 1.02×10−4 = Correct Part D Find the direction of the total force acting on the third charge. ANSWER: -0.557 = Correct between and +x-axis

Problem 21.68 Two identical spheres with mass

are hung from silk threads of length

, as shown in the figure

. Each sphere has the same charge, so . The radius of each sphere is very small compared to the distance between the spheres, so they may be treated as point charges. Part A

Suppose that the angle is small, and find the equilibrium separation between the spheres (Hint: If is small, then

.)

Express your answer in of the variables , ANSWER: = Correct

,

and appropriate constants.