Electric Charge Electric Fields Montwood High School Physics R. Casao

Electric Charge All matter is composed of atoms which contain negatively charged electrons, positively charged protons, and neutrons which have no charge. We will concern ourselves with the relative number of positive and negative charges because charges exert forces of attraction or repulsion on other charges. The movement of charges produce electric and magnetic fields. Law of electrostatics: like charges repel each other; unlike charges attract each other Repel: positive & positive; negative & negative. Attract: positive & negative.

Attraction & Repulsion Attraction – rods pulled toward each other. Repulsion – rods push each other away.

Electric Charge The electrostatic force of attraction is the force responsible for holding the protons and electrons together in the atom. Neutral objects have an equal number of positive and negative charge and do not exert forces on other charges and are not effected by other charges. Charge cannot be created, but can be transferred from one object to another. Charge is conserved. Everyday objects becomes charged by gaining or losing electrons, not protons.

Electric Charge The protons are held tightly within the nucleus by the strong nuclear force, even though the electromagnetic force of repulsion would push (repel) the protons within the nucleus. Other forces, like rubbing, can overcome the electrostatic force of attraction and remove electrons from an atom. Net gain in electrons results in negative charge; net loss in electrons results in positive charge. When one object gains a charge, another object loses the charge; the total electric charge on both bodies does not change.

Electric Charge The Transfer of Charge (Friction) SILK Glass Rod SILK Some materials attract electrons more than others.

Electric Charge The Transfer of Charge (Friction) - + SILK Glass Rod SILK - + As the glass rod is rubbed against silk, electrons are pulled off the glass onto the silk.

The Transfer of Charge (Friction) Electric Charge The Transfer of Charge (Friction) Glass Rod SILK - + + - Usually matter is charge neutral, because the number of electrons and protons are equal. But here the silk has an excess of electrons and the rod a deficit.

The Transfer of Charge (Friction) Electric Charge The Transfer of Charge (Friction) + Glass Rod SILK + - - - + - + - + Glass and silk are insulators; charges stuck on them stay put. Conductors allow charges to move through them. Charge distributes itself over the entire surface of the object. 1 3 1

Electric Charge

Electric Charge Gains or losses of electrons occur in whole numbers – you cannot gain or lose half an electron. In chemistry, used +1, -1, +2, -2, etc. to designate the charge on an ion. These numbers refer to the difference in the number of electrons and protons, not the actual charge on the ions. Symbol for charge is Q or q; unit is the Coulomb, C. Amount of charge on 1 proton: 1.602 x 10-19 C. Amount of charge on 1 electron: -1.602 x 10-19 C. The positive and negative charges will be used to identify forces between charges as attractive or repulsive. I don’t recommend using them in problems.

The electroscope is the simplest device used to determine electric charge. Consisting of a metal rod with a metallic bulb at one end, the rod is attached to a solid rectangular piece of metal that has an attached foil “leaf” made of aluminum. The arrangement is insulated from its protective glass container by a nonconducting frame. When charged objects are brought close to the bulb, electrons in the bulb are either attracted to or repelled by the charged objects. If a negatively charged rod is brought near the bulb, electrons in the bulb are repelled, and the bulb is left with a positive charge. The electrons are conducted down to the metal rectangle and the attached leaf, which will then swing away because they have like charges.

Figure 15-4 The electroscope An electroscope can be used to determine whether an object is electrically charged. When a charged object is brought near the bulb, the leaf moves away from the metal piece.

Charging By Induction Bringing a positively charged rod close to, but not touching, a neutral conducting sphere will cause the negative charges within the neutral sphere to be attracted to the positively charged rod and the positive charges within the neutral sphere to be repelled to the opposite side of the neutral sphere. The net charge on the sphere is still zero, but one end of the sphere is positively charged and the other end of the sphere is negatively charged. A ground is a conducting path between an object and the Earth to prevent electric shock due to excess charge.

Charging By Induction The Earth is a conductor and can act as a source for extra electrons or as a sink for unwanted electrons. Electrons from the Earth will move up the conductor and cancel out the positive charges on the sphere. Once the positive charges on the sphere have been neutralized, leaving only the negative charges on the sphere, the force of repulsion prevents additional electrons from moving onto the sphere. The sphere is now negatively charged.

21-2 Schematic diagram of the operation of a LASER PRINTER

Charge Neutralization When two charged objects are allowed to touch, charge neutralization occurs. If object A has a charge of 16 C and object B has a charge of -4 C and they are connected by a wire, charge can flow between the objects and 4 of the positive charges will cancel the 4 negative charges. A charge of 12 C will remain and due to the force of repulsion, the positive charges will try to get as far away from each other as possible, so 6 C will go to object A and 6 C will go to object B. Remove the connecting wire and both object A and object B have a charge of 6 C.

Coulomb’s Law Coulomb’s law describes the electric force between any two charges, separated by a distance d. k is a constant that considers the effect of the material between the charges on the force. Force measured in N; for air or a vacuum, k = 8.9875 x 109 Many charges are expressed in micro-coulombs (C); 1 x 106 C = 1 C. Easiest solution, whenever you see C, just add x 10-6 C to the number. Ex. 5 C = 5 x 10-6 C; 28 C = 28 x 10-6 C.

Coulomb’s Law Example Two electrostatic point charges of 60 C and 50 C exert a repulsive force on each other of 175 N. What is the distance between the two charges? Q1 = 60 x 10-6 C; Q2 = 50 x 10-6 C.

Superposition of Forces from Two Charges Light blue charges fixed , negative, equal charge (-q) What is force on positive charge +q at origin? x y 6 8 12

Superposition of Forces from Two Charges Light blue charges fixed , negative, equal charge (-q) What is force on positive charge +q at origin? Consider effect of each charge separately: y x 6 13 9

Superposition of Forces from Two Charges Light blue charges fixed , negative, equal charge (-q) What is force on positive charge +q at origin? Take each charge in turn: y x 7 14 10

Superposition of Forces from Two Charges Light blue charges fixed , negative, equal charge (-q) What is force on positive charge +q at origin? Create vector sum: y x 8 15 11

Superposition of Forces from Two Charges Light blue charges fixed , negative, equal charge (-q) What is force on positive charge +q at origin? Find resultant: y NET FORCE x 9 16 12

Superposition Principle F13 F31 F31 F F31y q1 F21 q2 F31x F21 q3 F21y Forces add vectorially F21x F = (F21x + F31x) x + (F21y + F31y) y Everything you learned about vectors applies to the forces between charges! 10 14 18

Conductors and Insulators Conductor transfers charge on contact Insulator does not transfer charge on contact Semiconductor might transfer charge on contact

Charge Transfer Processes Conduction Polarization Induction

Metals and Conduction Notice that metals are not only good electrical conductors, but they are also good heat conductors, tend to be shiny (if polished), and are maleable (can be bent or shaped). These are all properties that come from the ability of electrons to move easily. This iron atom (26 protons, 26 electrons) has two electrons in its outer shell, which can move from one iron atom to the next in a metal. Path of electron in a metal

Electric Fields An electric field is a region around one charged object in which a second charged object will experience an electric force of repulsion or attraction. If a small test charge qo is placed near a charge Q, the test charge qo is repelled by Q with a force F. The electric field strength at the location of qo is:

Electric Fields Units for electric field: N/C. The direction of the electric field E depends on the sign of the charge producing the field. Electric field lines point away from positive charges. Electric field lines point towards negative charges. The greater the number of electric field lines, the stronger the electric field.

Electric Field Strength Electric field strength can also be determined using the charge Q that is producing the electric field: The distance from the charge to the point at which we want to determine the electric field strength is d. Electric field is a vector, so everything you learned about vectors applies!

Electric Fields and Acceleration Electric fields can be used to accelerate charged particles, such as protons and electrons. Charge on proton or electron, qo = 1.602 x 10-19 C Mass electron = 9.11 x 10-31 kg Mass of proton = 1.67 x 10-27 kg Can use the old velocity equations to find whatever you need to:

Electric Field Example A proton and an electron in a hydrogen atom are separated by about 5.3 x 10-11 m. What is the magnitude and direction of the electric field set up by the proton at the position of the electron? Known values: k = 8.9875 x 109 N·m2/C2; Q = 1.602 x 10-19 C; d = 5.3 x 10-11 m. Direction: the proton is positive and electric field lines extend outward away from positive charges, so the electric field produced by the proton at the position of the electron is away from the proton.

Electric Field Example If the electron could be accelerated in the electric field produced by the proton, what is the acceleration of the electron and what is the speed of the electron after 0.5 s, assuming the electron starts from rest? Known values: mass electron = 9.11 x 10-31 kg; charge electron = 1.602 x 10-19 C; E = 5.12566 x 1011 N/C

Forces on electron beam in a TV tube (CRT) F = Q E and F = m g (vector equations) 24-22 Forces in a TV tube

Motion of a Charged Particle in a Uniform Electric Field If the electric field E is uniform (magnitude and direction), the electric force F on the particle is constant. If the particle has a positive charge, its acceleration a and electric force F are in the direction of the electric field E. If the particle has a negative charge, its acceleration a and electric force F are in the direction opposite the electric field E. September 18, 2007

An Accelerated Electron An electron enters the region of a uniform electric field as shown in the figure, with vi = 3 x 106 m/s and E = 200 N/C. The horizontal length of the plates is l = 0.1 m. A. Find the acceleration of the electron while it is in the electric field.

If the electron enters the field at time t = 0 s, find the time at which it leaves the field. If the vertical position of the electron as it enters the field is yi = 0 m, what is its vertical position when it leaves the field?

Because the electron is deflected downward between the plates by the electric field, the final y position for the electron is -0.0195 m below its initial y position.

TV tube with electron-deflecting charged plates (orange) F = Q E