Physics 122B Electricity and Magnetism

Physics 122B Electricity and Magnetism Lecture 1Charge and Coulomb’s LawMarch 26, 2007 Martin Savage

This week Physics 122B - Lecture 1

The History of Electricity ElectricÞelektron = Greek word for amber “Rub amber with wool, and it will pick up bits of wood, feathers, straw …” Thales of Miletus (640-546 BC) About 1736, Charles Francois du Fay (1698-1739) learned that rubbing glass and rubbing resinous substances (e.g., amber) seemed to produce charges of different kinds. He found that two charges of the same kind repelled each other, while two of unlike kinds attracted. He suggested that electricity might exist as two distinctly different types, which he named “vitreous” and “resinous” electricity. William Watson (1715-1790) suggested in 1746 that electricity was one “fluid”. One of the two kind of electricity proposed by Du Fay could be an excess (+) of this fluid and the other a difficiency of it (-). Flow from + to - could account for electrical discharge. Benjamin Franklin (1706-1790) adopted and popularized Watson's “one fluid” theory and chose vitreous electricity to be the positive type (thereby giving electrons a negative charge). Franklin’s great reputation won universal acceptance for this view. Physics 122B - Lecture 1

Charging Experiments (1) 1 2 • Observations: • No force is observed between un-rubbed rods. • Plastic rods rubbed with wool repel each other. • Glass rod rubbed with silk attracts plastic rod rubbed with wool. • At increased distance, forces are decreased. 4 3 Physics 122B - Lecture 1

Charging Experiments (2) 1 3 2 • More Observations: • A (charged) plastic rod rubbed with wool attracts small pieces of paper. • A (charged) plastic rods rubbed with wool is attracted to an un-rubbed (neutral) plastic rod. • A plastic rod rubbed with wood is attracted to the wool, repelled by the silk. • No charged (rubbed) object attracts both the charged plastic rod and the charged glass rod. 4 Physics 122B - Lecture 1

Charging Experiments (3) 1 2 3 • Even More Observations: • The charge from a plastic rod rubbed with wool can be transferred to a metal sphere. • After the transfer, the plastic rod does not attract paper. • A 2nd metal sphere connected by a metal rod acquires the rod’s charge. • A 2nd metal sphere connected by a plastic rod does not acquire the rod’s charge. 4 Physics 122B - Lecture 1

Electric Charge and Atoms An atom with atomic number Z consists of a small but massive nucleus of charge +Ze, surrounded by a cloud of Z electrons, each with much less mass and with a charge of -e. The atom has a diameter of about 10-10 m (0.1 nm), while the atomic nucleus has a diameter of about 5x10-15 m (5 fm). All atoms, heavy or light, are about the same size, but the mass varies from 1 to ~250. The nucleus contains Z protons with charge +e and N neutrons with charge 0. The atomic mass number of the atom is A = Z+N. Charge: q = Npe-Nee = (Np-Ne)e ; for neutral atoms (q=0), Np=Ne=Z Physics 122B - Lecture 1

Positive and Negative Ions Atoms can have a net charge ifNp¹Ne, whereNp=Zis the number of protons andNeis the number of electrons in the atom. If a neutral atom loses one electron, it will have a net positive charge ofq=+e because Np-Ne=+1. If a neutral atom gains one electron, it will have a net negative charge of q=-e because Np-Ne=-1. Physics 122B - Lecture 1

Charging by Friction Friction causes the breaking of molecular bonds, and can result in a separation of charges in a formerly neutral molecule, creating a positive and a negative molecular ion. Rubbing a plastic rod with wool or a glass rod with silk produces such charge separation effects. Physics 122B - Lecture 1

Conservation of Charge Electrical charge can be neither created or destroyed. It can be separated and moved around, but the net charge of an isolated system must remain constant.qinitial = qfinal Example: A plastic rod is rubbed with wool, each initially neutral. Thenqwool=-qrod. Physics 122B - Lecture 1

Insulators and Conductors (1) If a conductor is charged, all of the charge must reside on the outer surface (and none in the interior.) If an insulator is charged, the charge may (or may not) reside in the interior. Physics 122B - Lecture 1

Insulators and Conductors (2) In insulators, the electrons are tightly bound in the atoms and are not free to move around. When insulators are charged, e.g. by friction, patches of molecular ions are created on the surface, but these patches are immobile. In solid metal conductors, the outer (valence) electrons of the atoms are only weakly bound and are free to move around in the solid. The conductor as a whole may be electrically neutral, but the electrons are rather like an electrically charged liquid, a “sea” of electrons within the material. Electrons are the “charge carriers”. There are other forms of conduction (in ionic liquids, etc.) in which the charge carriers are not electrons. Physics 122B - Lecture 1

Charging an Insulator Physics 122B - Lecture 1

Charging a Conductor Conductors cannot be charged by friction. However, charge can be transferred to a conductor by contact with a charged object. The charges arriving at the conductor stay on the outer surface and distribute themselves over that surface so that they are as far away as possible from the repulsive forces of the other charges. Physics 122B - Lecture 1

The Electroscope Physics 122B - Lecture 1

Charging an Electroscope The angle of deflection of the leaves provides a rough indication of the amount of charge that has been deposited on the electroscope. Physics 122B - Lecture 1

Discharging a Charged Object The human body, composed mainly of salty water, is a moderately good conductor. Therefore, a person touching a charged object will normally discharge the object. Where the charge goes next depends on the degree to which the person is insulated from ground (e.g., by rubber shoe soles). Physics 122B - Lecture 1

Charge Polarization Physics 122B - Lecture 1

Induced Charge By using charge polarization, it is possible to induce charge on an electrically neutral object. Example: Bring a charged rod near (but not touching) an electroscope and observe the effect on the leaves. -- - - - - - - + + + + + + Physics 122B - Lecture 1

Charges and Forces Physics 122B - Lecture 1

The Electric Dipole Experiment: Bring a positive charge near a neutral atom. Physics 122B - Lecture 1

Dipoles and Forces (1) Physics 122B - Lecture 1

Dipoles and Forces (2) Physics 122B - Lecture 1

Charging by Induction Induction: Charging an object with only neutral contact. Physics 122B - Lecture 1

Coulomb’s Law Like charges repel. Charles Augustine de Coulomb (1736-1806). Opposite charges attract. ( Magnitude of force ) Coulomb’s Law: Physics 122B - Lecture 1

Units of Charge Coulomb’s Law, written two ways. (Note that in Newton’s law of gravitation, G, which plays a role similar to K, has the valueG = 6.67 ´10-11 N m2/kg2.) Physics 122B - Lecture 1

Using Coulomb’s Law • Coulomb’s Law applies only to point charges. • (This is particularly important because charge are free to move around on conductors.) • Strictly speaking, Coulomb’s Law applies only to electrostatics (non-moving charges). • (However, it is usually OK provided v<<c). • Electrostatic forces can be superposed. • Linear superposition !!!! Physics 122B - Lecture 1

Example: Sum of Two Forces Two +10 nC charged particles are 2 cm apart on the x axis. (1) What is the net force on a +1.0 nC particle midway between them? (2) What is the net force if the charged particle on the right is replaced by a -10 nC charge? -9 9 Physics 122B - Lecture 1

Example: Point of Zero Force Two positively charged particles q1 and q2=3q1 are placed 10. 0 cm apart. Where (other than infinity) could another charge q3 be placed so as to experience no net force? Need force vectors to be co-linear, so location must be on x axis. Need force vectors to be in opposite directions, so location must be between 0 and d. Need force vectors equal in magnitude, so F=Kq1q3/x2=Kq2q3/(d-x)2. Therefore,(d-x)2=3x2orx=d/(1±√3) = 10 cm/(1±1.732); x+=10.0 cm/2.732 = 3.66 cm; x-=10.0 cm/-0.732=-13.66 cm, which does not satisfy the 2nd criterion. Physics 122B - Lecture 1

Example: Three Charges (1) Three charges with q1 = -50 nC, q2 = +50 nC, and q3 = +30 nC, are placed at the corners of a 10 cm x 5 cm rectangle as shown. What is the net force on q3 due to the other two charges? Physics 122B - Lecture 1

Example: Three Charges (2) Cos q Sin q Physics 122B - Lecture 1

Example: Lifting a Glass Bead A small plastic sphere is charged to -10 nC. It is held 1.0 cm above a small glass bead that rests on a table. The bead has a mass of 15 mg and a charge of +10 nC. Will the glass bead “leap up” to the plastic sphere? Therefore, F1 on 2 exceeds w by a factor of 60. Therefore, the sphere should indeed leap upward. (Note that we have neglected electrical forces between the bead and table, which could be significant.) Physics 122B - Lecture 1

End of Lecture 1 • Before the next lecture, read Knight, Chapters 25.5 through 26.1 • Lecture Homework #1 will be placed on the Tycho system soon.

Physics 122B Electricity and Magnetism