1-muatan-listrik3.pptx

Welcome to Physics 112!

Law of Electrical ForceCharles-Augustin Coulomb(1785)" The repulsive force between two small spheres charged with the same sort of electricity is in the inverse ratio of the squares of the distances between the centers of the spheres"

q2q1r17Lecture 1#What We CallCoulomb's LawMKS Units:r in metersq in Coulombs in Newtons is a unit vector pointing from 1 to 2 This force has same spatial dependence as the gravitational force, BUT there is NO mention of mass here!! The strength of the force between two objects is determined by the charge of the two objects, and the separation between them.

q2q1The force from 1 acting on 2

We call this group of constants k as in:14= 9 109 N-m2/C20

28Lecture 1#Coulomb Law Qualitativeq2rq1 What happens if q1 increases? F (magnitude) decreases F (magnitude) increases

What happens if q1 changes sign ( + - )?

The direction of is reversed

What happens if r increases?

3Lecture 1#A charged ball Q1 is fixed to a horizontal surface as shown. When another massive charged ball Q2 is brought near, it achieves an equilibrium position at a distance d12 directly above Q1.When Q1 is replaced by a different charged ball Q3, Q2 achieves an equilibrium position at distance d23 (< d12) directly above Q3.Q2Q1gd12Q2d23Q31a: A) The charge of Q3 has the same sign of the charge of Q1 B) The charge of Q3 has the opposite sign as the charge of Q1 C) Cannot determine the relative signs of the charges of Q3 & Q1

1b: A) The magnitude of charge Q3 < the magnitude of charge Q1 B) The magnitude of charge Q3 > the magnitude of charge Q1 C) Cannot determine relative magnitudes of charges of Q3 & Q1

4Lecture 1#Q2Q1gd12Q2d23To be in equilibrium, the total force on Q2 must be zero.The only other known (from 111) force acting on Q2 is its weight.Therefore, in both cases, the electrical force on Q2 must be directed upward to cancel its weight.Therefore, the sign of Q3 must be the SAME as the sign of Q1Q3A charged ball Q1 is fixed to a horizontal surface as shown. When another massive charged ball Q2 is brought near, it achieves an equilibrium position at a distance d12 directly above Q1.When Q1 is replaced by a different charged ball Q3, Q2 achieves an equilibrium position at distance d23 (< d12) directly above Q3.1a: A) The charge of Q3 has the same sign of the charge of Q1 B) The charge of Q3 has the opposite sign as the charge of Q1 C) Cannot determine the relative signs of the charges of Q3 & Q15Lecture 1#Q2Q1gd12Q2d23Q3The electrical force on Q2 must be the same in both cases it just cancels the weight of Q2 .

Since d23 < d12 , the charge of Q3 must be SMALLER than the charge of Q1 so that the total electrical force can be the same!!A charged ball Q1 is fixed to a horizontal surface as shown. When another massive charged ball Q2 is brought near, it achieves an equilibrium position at a distance d12 directly above Q1.When Q1 is replaced by a different charged ball Q3, Q2 achieves an equilibrium position at distance d23 (< d12) directly above Q3.1b: A) The magnitude of charge Q3 < the magnitude of charge Q1 B) The magnitude of charge Q3 > the magnitude of charge Q1 C) Cannot determine relative magnitudes of charges of Q3 & Q1

6Lecture 1#Gravitational vs. Electrical ForceFelecFgrav = q1q2m1m2 14pe0GrFFq1m1q2m2Felec = 14pe0 q1q2r2 Fgrav = G m1m2r2 * smallest charge seen in nature!For an electron:* |q| = 1.6 10-19 Cm = 9.1 10-31 kgFFelecgrav=+4171042.7Lecture 1#Notation For Vectors and ScalarsVector quantities are written like this : F, E, x, rTo completely specify a vector, the magnitude (length) and direction must be known.rrWhere Fx, Fy, and Fz (the x, y, and z components of F ) are scalars.

A unit vector is denoted by the caret ^. It indicates only a directionand has no units.

The magnitude of is ; this is a scalar quantity

The vector can be broken down into x, y, and z components:

For example, the following equation shows specified in terms of , q1, q2, and r :

8Lecture 1#Vectors: an ExampleNow, plug in the numbers. F12 = 67.52 N

To do this, use Coulombs Law:

q1 and q2 are point charges, q1 = +2mC and q2 = +3 mC. q1 is located at and q2 is located at

Find F12 (the magnitude of the force of q1 on q2).

y (cm)x (cm)1 2 3 4321q1q2r9Lecture 1#Vectors: an Example continuedNow, find Fx and Fy, the x and y components of the force of q1 on q2.y (cm)x (cm)1 2 3 4321q1q2rq

SymbolicallyNow plug in the numbersFx = 47.74 NFy = 47.74 N

10Lecture 1#What happens when youconsider more than two charges? What is the force on q when both q1 and q2 are present??The answer: just as in mechanics, we have the Law of Superposition:The TOTAL FORCE on the object is just the VECTOR SUM of the individual forces.

F F1 F2q+q1+q2 If q2 were the only other charge, we would know the force on q due to q2 . If q1 were the only other charge, we would know the force on q due to q1 . F = F1 + F21111Lecture 1#Two balls, one with charge Q1 = +Q and the other with charge Q2 = +2Q, are held fixed at a separation d = 3R as shown. +2Q+2QQ2Q13R+QRQ2Q1+QQ32R(a)The force on Q3 can be zero if Q3 is positive.(b)The force on Q3 can be zero if Q3 is negative.(c)The force on Q3 can never be zero, no matter what the (non-zero!) charge Q3 is. Another ball with (non-zero) charge Q3 is introduced in between Q1 and Q2 at a distance = R from Q1. Which of the following statements is true?1212Lecture 1#Two balls, one with charge Q1 = +Q and the other with charge Q2 = +2Q, are held fixed at a separation d = 3R as shown. Another ball with (non-zero) charge Q3 is introduced in between Q1 and Q2 at a distance = R from Q1.Which of the following statements is true?The magnitude of the force on Q3 due to Q2 is proportional to (2Q Q3 /(2R)2) The magnitude of the force on Q3 due to Q1 is proportional to (Q Q3 /R2) These forces can never cancel, because the force Q2 exerts on Q3 will always be 1/2 of the force Q1 exerts on Q3!!(a)(c)(b)The force on Q3 can be zero if Q3 is positive.The force on Q3 can be zero if Q3 is negative.The force on Q3 can never be zero, no matter what the (non-zero) charge Q3 is.Q2Q13R+QRQ2Q1+QQ32R13Lecture 1#Another ExampleWhat is the force acting on qo ( ) ?qo, q1, and q2 are all point charges where qo = -1mC, q1 = 3mC, and q2 = 4mC. Their locations are shown in the diagram.

What are F0x and F0y ?Decompose into its x and y components

x (cm)y (cm)1 2 3 4 5 4321qoq2q1qWe have

14Lecture 1#Another Example continuedqo, q1, and q2 are all point charges where qo = -1mC, q1 = 3mC, and q2 = 4mC. Their locations are shown in the diagram.

Now add the components of andto find and

x (cm)y (cm)1 2 3 4 5 4321qoq2q1

15Lecture 1#Another Example continuedqo, q1, and q2 are all point charges where qo = -1mC, q1 = 3mC, and q2 = 4mC. Their locations are shown in the diagram.

The magnitude of is

x (cm)y (cm)1 2 3 4 5 4321qoq2q1

Lets put in the numbers . . .

16Lecture 1#What is a Field?A FIELD is something that can be defined anywhere in spaceA field represents some physical quantity (e.g., temperature, wind speed, force)It can be a scalar field (e.g., Temperature field)It can be a vector field (e.g., Electric field)It can be a tensor field (e.g., Space-time curvature)Electric field, introductionOne problem with the above simple description of forces is that it doesnt describe the finite propagation speed of electrical effects.In order to explain this, we must introduce the concept of the electric field.17Lecture 1#

77828368556683758090917571807284738288927788887364A Scalar FieldThese isolated temperatures sample the scalar field(you only learn the temperature at the point you choose,but T is defined everywhere (x, y)18Lecture 1#

77828368556683758090917571807284735788927756887364A Vector FieldIt may be more interesting to know which way the wind is blowing...That would require a vector field(you learn both wind speed and direction)It may be more interesting to know which way the wind is blowing19Lecture 1#SummaryCharges come in two varietiesnegative and positivein a conductor, negative charge means extra mobile electrons, and positive charge means a deficit of mobile electrons

Coulomb Forcebi-linear in chargesinversely proportional to square of separationcentral force

Law of Superposition F = F1 + F2 Fields20Lecture 1#Appendix A: Electric Force ExampleSuppose your friend can push their arms apart with a force of 100 lbs. How much charge can they hold outstretched?+Q-Q2mF= 100 lbs = 450 N

= 4.4710-4 C

Thats smaller than one cell in your body!

21Lecture 1#Appendix B: Outline of physics 212Coulombs Law gives force acting on charge Q1 due to another charge, Q2.

superposition of forces from many charges

Electric field is a function defined throughout space

here, Electric field is a shortcut to Force

later, Electric field takes on a life of its own!

Q1Q2Q3

22Lecture 1#