- Like charges repel Induced Charge. or by induction. Electric charge is conserved

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1 Course website: Here you will find the syllabus, lecture notes and other course information Links to the website are also on Blackboard: Phys 112 (Spring 2017) (Announcements will appear here) Required items: 1. Text book Physics: Principles with Applications, 7 th ed, Vol 2. by Giancoli. Available in printed form or as an ebook with Mastering Physics 2. Access to Buy access directly at or get an access code from the Univ. Bookstore Register at (for the online homework) Course ID = FRETWELLSPRING2017 Student ID = your ISU Net ID (i.e. first part of your ISU address) The Lab manual is online. You can find this and other Lab info on Blackboard at Phys 112 LABS (Spring 2017) Electric Force Coulomb s Law Electric Charge Its Conservation In the Atom Insulators and Conductors Induced Charge Electroscope Electric Field Field Lines E fields and conductors Gauss s Law 16.1 Static Electricity; Electric Charge and Its Conservation Electric charge is an intrinsic property of some elementary particles Charge comes in two types: and Objects can be charged by rubbing (which moves electrons from one object to the other) A neutral object has equal amounts of and charge A negatively charged object has an excess of charge A positively charged object has lost some of its charge Net charge = sum of all and charges in an object Free charges are loosely bound electrons that can move freely around a conductor Triboelectric series Most positively charged Human skin Rabbit's fur Glass Human hair Nylon Wool Lead Cat's fur Silk Aluminium Paper(Small positive charge) Cotton (No charge) Steel(No charge) Wood(Small negative charge) Amber Polystyrene Rubberballoon Brass Gold Synthetic rubber Styrofoam Most Plastic wrap negatively charged [not for the exam] Scotch tape PVC rubber 0 Static Electricity; Electric Charge and Its Conservation 16.4 Induced Charge Like charges repel Opposite charges attract. Metal objects can be charged by conduction, or by induction. Electric charge is conserved i.e. the net charge produced in any process is zero In a conductor (e.g. a metal), charge flows freely Almost no charge flows in an insulator Semiconductors (e.g. Si) have an intermediate conductivity Neutral metal rod acquires a charge when it is touched by a charged metal object. We can see induction in conductors because it gives rise to a net attractive interaction Charge is induced at each end of the metal rod. 1

2 Induced Charge Ground or Earth = reservoir where charge moves freely to/from Induced Charge To get a permanent charge on the metal rod by induction a path must be provided for charge to flow Charge separation can also be induced inside the atoms or molecules of a nonconductor where it again gives rise to a weak attractive interaction Cut the wire with the charged object nearby. Atom or molecule electrophorus The rod is now permanently charged. It has the opposite charge to the original charged object. so balloons stick to walls. The Electroscope A charged electroscope can be used to determine the sign of an unknown charge. First charge it by induction or conduction. Then bring the unknown charge close to the electroscope. A metal ball hangs from the ceiling by an insulating thread. The ball is attracted to a positivecharged rod held near the ball. The charge of the ball must be: 1. Only positive 2. Only negative 3. Only neutral 4. Positive or neutral 5. Negative or neutral Same charge Leaves open more Opposite charge Leaves close 16.5 Coulomb s Law Coulomb s Law The magnitude of the electric force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. Units = Coulomb (161) Insignificant volume k = Nm 2 /C 2 Units of charge = Coulomb, C k can also be written in terms of ε 0, the permittivity of free space aka Electric constant = 1 4 = / The electric force is typically much stronger than the gravitational force Force acts along the line connecting the charges. force on 1 due to 2 Same charges repel force on 2 due to 1 Opposite charges attract 1C 2 C Which charge feels the bigger force? 2

3 Coulomb s Law All electrons have the same charge: Smallest isolated charge found in nature Electric charge is quantized in units of the electron charge, e. Charges produced by rubbing are typically around a microcoulomb: ~ electrons ~ 10 6 C To calculate the Net Force on a charge Example: What is the y net force acting on the negative charge? 40 o 140 N θ 850 N 10 o x =850 cos cos(50) =850 sin sin(50) And the direction is given by, Magnitude of resultant force is, = Force is a vector quantity 1. Draw a picture and roughly determine the net force 2. Calc. the components of force acting on a charge due to all other charges 3. Add the x and y components of the forces separately: = above the x axis Take care when working in other quadrants 16.7 The Electric Field How big are the Electric fields around us? Electric field is defined to be the force felt by a small positive test charge, q, divided by that charge: Small enough not to disturb charges that created E If q is positive,eand F point in the same direction Units N/C (163) If q is negative, E and F point in opposite directions Note, E does not depend on q it depends on the charges that produce the electric field. Near the Earth s surface Electrical breakdown in air electron ~150N/C 3,000,000 N/C proton 5 x N/C Inside a hydrogen atom Near a comb ~1000 N/C 3 x N/C 92 protons Near a Uranium nucleus Electric Field For a point charge: [magnitude] (164a) A small 4.0 µc charge sits in a uniform electric field and feels a downward (electric) force of 6.0 N. What is the electric field at this point (ignore gravity)? F = 6.0 N 4.0 µc E is a vector that points away from () charges... Electric field (like force) is a vector. Components can be added to give the net electric field at a point and towards () charges x 10 6 N/C UP x 10 6 N/C DOWN x 10 7 N/C UP x 10 7 N/C DOWN 5. E = kq/r 2 3

4 The Electric Field Problem solving in electrostatics: Electric forces and electric fields 1. Draw a diagram. (show all charges with signs, and fields and forces with directions) 2. Calculate all components of forces or fields. = ; or = for point charges 3. Add forces or fields vector components to get resultant. Example. Calculate the electric field near a dipole Field at B: E 1 = (9x10 9 )(50x10 6 )/ = 2.86x10 6 N/C From geometry, and are 49 o E 2 = (9x10 9 )(50x10 6 )/ = 2.86x10 6 N/C above and below the horizontal Add x and y components: x y B 49 o 49 o E x10 6 cos x10 6 sin49 E x10 6 cos x10 6 sin49 E 3.75x cm = ( ) 1 2 = / 26 cm In the x direction. 50 µc 50 µc Example. Calculate the electric field near a dipole OR Use the symmetry: and have same magnitude Is there a point on the line where E = 0? B 49 o 49 o So we can immediately write down the answer E = 2 E 1 cos49 = / In the x direction. Q 2Q 10 cm 30 cm µc 26 cm 50 µc Generally, θ θ ½ the angle between the 2 vectors Sum of any 2 vectors of equal magnitude is E = 2 E 1 cosθ What happens if a 3 rd charge is placed at that point? What if the two charge have the same sign? 16.8 Field Lines Field Lines: near point charges The electric field can be represented by field lines. Field lines start on () charges and end on () charges. Field lines never cross The field at a point is a vector tangential to the field line there. Electric dipole Two charges of different magnitude and opposite sign. E.g. Electric dipole (two opposite charges) Electric field is stronger when the field lines are closer together. Two charges of the same magnitude and sign. Magnitude of point charge Number of field lines starting/ending on that charge. Where is E = 0 in these figures? 4

5 Field Lines: inside a capacitor 16.9 Electric Fields and Conductors The electric field between two closely spaced, oppositely charged parallel plates is UNIFORM (same value everywhere) Static electric field inside a solid conductor is zero If it were not, the charges inside the conductor would feel a force and move around in order to make E zero. E = 0 Field lines are equally spaced = = Can be derived using Gauss s Law. Any net charge in a conductor distributes itself on the surface. Electric field is perpendicular to the outer surface of a conductor Solid metal sphere with Q net charge E (each plate carries charge Q and has area A) if it were not, charges would move to make it perpendicular. Electric Fields and Conductors What are some of the consequences of this? Inner surface Q Neutral conducting Outer surface Q shell Electric Fields and Conductors Now let the shell carry some charge.. Q 3Q A 3Q point charge is at the center of hollow conducting spherical shell. Shell has net charge of Q. What is the charge on the outer surface of the shell? Q E = 0 inside Field lines radiate out from the central 3Q charge. 3Q appears on inner surface If a point charge Q is placed at the center of a NEUTRAL hollow conducting shell, the E field induces a separation of charge in the shell. From the outside it looks as though the shell is not there = inner outer = 3 outer 2Q appears on outer surface E field outside shell is identical to one that would be produced by a 2Q point charge, (= 3Q Q) at the center of the shell E field outside any charged spherical conductor (solid or hollow) is the same as if all the charge were concentrated at the center of the sphere. Electric Fields and Conductors Application: Faraday cage used to shield people and equipment from external electric fields Gauss s Law Gauss s Law can be used to calculate E Introduce a new concept.. Electric flux Between and area normal (167) Electric flux through an area is proportional to the number of field lines crossing the area. 5

6 Gauss s Law Total Flux through (an imaginary) closed surface, Gauss s Law Total electric flux passing through a closed surface is proportional to the charge enclosed by that surface. Zero flux flows through closed surface Flux in (left) = Flux out (right) Net flux flows out of closed surface By convention, flux is positive if it s coming out of a closed surface Total electric flux through closed surface charge enclosed by closed surface Gauss s Law (169) Double charge enclosed double the flux through the closed surface Gauss s Law can be used to find the electric field in situations with a high degree of symmetry [there will be no derivations using Gauss s Law in the Exam] Ex Calc. E field using Gauss s Law for a charged metal shell of radius r 0 with net charge Q. Outside the shell: imagine a spherical closed surface, 1 0 Charge enclosed by 1 Σ E A = E Σ A = E(4πr2 ) = Q/ε 0 so = /4 0 2 Inside the shell: imagine surface 2 0 Charge enclosed by 2 = 0 So = 0 < 0 0 r A 2 A 1 r Two kinds of electric charge positive and negative Charge is conserved Charge on electron: Charge is quantized in units of e Conductors: electrons free to move Objects can be charged by conduction or induction Coulomb s law: Electric field is force per unit charge: Electric field of a point charge, Q: Summary of Chapter 16 So, E field outside a charged spherical shell is the same as if all the charge were concentrated at the center of the shell. What if the shell was a solid sphere instead? E r 0 ~ 1/r 2 r Electric field can be represented by electric field lines Static electric field inside conductor is zero; surface field is perpendicular to surface Electric flux: Gauss s law: 6