Chapter 18 Electrostatics Electric Forces and Fields Electrical charges that does not flow through an object, but sit stationary on the surface of an object. Usually it is isolated on the surface, but can transfer from object to object by contact. Protons and Electrons both have electrical charges that are equal even though their masses are quite different. It is: Qe = 1.6 X 10-19 Coulombs 1C (very large unit so often use µc) = 6.25 X 10 18 electrons
Charges can be transferred simply by rubbing electrons off of atoms outer shell or valence electrons. Protons don t move, only electrons. + charge by deficiency of e - - charge by over abundance of e - Electrons always move through material from negative to positive charge by conduction and induction. All natural objects prefer to be neutral with the same number of protons as electrons, causing electrons to jump to areas where there is a deficiency of electrons or + charge.
BECAUSE: 1. All Electrical charges (q) occur as multiples of the electrical charge on a single electron in Coulombs, and 2. The Law of Conservation of Electric Charge states that within an isolated system the net electric charge remains constant. WE CAN CONCLUDE: Charges occur when Electrons are transferred from one object to another including into and out of the Earth and that they exert forces on each other as a result of this transfer. Electrostatic Force is the force that point charges exert on each other. It is one of the four fundamental forces of nature. It is much stronger than gravity even. There are two forces because each charged object acts on the other charged object. The forces are equal in magnitude and opposite in direction whether attractive or repulsive. LIKE CHARGES REPEL EACH OTHER AND UNLIKE CHARGES ATTRACT EACH OTHER.
Insulators and Conductors. Conductors are materials through which electric charges can move under the influence of electric forces; and. Insulators are materials that do not readily allow charges to move. Examples: *not clear cut relative values* CONDUCTORS: copper, aluminum, silver, gold, platinum, metals, carbon, INSULATORS: glass, rubber, vacuum, air.. On an irregularly shaped conductor, charge tends to accumulate at locations where the curvature of the surface is greatest, that is at sharp points and the amount of charge/area is greater than the flat end. At the sharp end the forces of repulsion between like charges are directed predominately away from the surface. As a result, the large force directed away from the surface can be great enough to cause the charge to jump from the surface into the surrounding air. This is how sharp-tipped Lightning rods work. They are designed to leak off excess charge before they build up, preventing Lightning from being attracted to the object.
Charging an Object by Direct Contact
Charging an Object by Induction When an object is charged by induction, it gains a charge that is opposite in sign to the charging rod!!
Coulomb s Law The magnitude of F between 2 point charges is directly proportional to the product of the two charges and inversely proportional to the square of the distance between them. This Law is closely related to Newton s Law of Gravitation, although gravity is only an attractive force. F = K q 1 q 2 K = 8.99 X 10 9 N m 2 /c 2 r 2 (from text) 8. The nucleus of the helium atom contains two protons that are separated by about 3 x 10-15 m. Find the magnitude of the electrostatic force that each proton exerts on the other. Is it an attractive or repulsive force?
10. In a vacuum, two particles have charges of q 1 and q 2, where q 1 = +3.5 m C. They are separated by a distance of 0.26 m, and particle 1 experiences an attractive force of 3.4N. What is q 2 (magnitude and sign)? 20. Two positive charges, when combined, give a total charge of +9.00 m C. When the charges are separated by 3.00 m, the force exerted by one charge on the other has a magnitude of 8.00 x 10-3 N. Find the amount of each charge.
Electric Field An electric Field (E) exists at a point as an electrostatic force experienced by a small test charge q 0 which is placed at that point divided by the amount of the test charge itself. The unit for electric field is : newton/coulomb (N/C). The field is a vector and always points in the same direction as a force on a positive test charge. The electrostatic force experienced by the test charge is the result of other charges surrounding it from various locations. If we combine Coulomb s law with the electric field equation, the test charge is eliminated from the equation leaving: E = kq, the electric field doesn t depend on the test charge. r 2
Information about the direction and magnitude of the electric field can be deduced if the charges making it up form some symmetrical pattern.
The figure below shows three (-) point charges and a (+) point charge along with some of the field lines drawn between them. They are drawn incorrectly. Examine how they are wrong and draw them correctly.
26. Charges of 4q are fixed on opposite corners of a square. A +5q is fixed to one of the remaining corners and +3q is fixed to the last corner. Assuming ten electric field lines emerge from the +5q charge, sketch the field lines in the vicinity of the four charges. 28. Two charges are placed on the x axis. One charge (q 1 = +8.5 mc) is at x 1 = +3.0 cm and the other (q 2 = -21 mc) is at x 1 = +9.0 cm. Find the net electric field (magnitude and direction) at x= 0 cm. 30. An electric field with a magnitude of 160 N/C exists at a spot that is 0.15 m away from a charge. At a place that is 0.45 m away from this charge, what is the electric field strength? 31. A 3.0Uc point charge is placed in an external uniform electric field of 1.6 x 10(4) N/C. At what distance from the charge is the net electric field zero?
FIELD LINES Around an Electric Dipole (a +q and q point charge slightly separated from each other) Field Lines (Lines of Force) 1. Always emanate from the + charge and travel to the charge, never stopping between charges, but always going the distance to next charge. 2. Field Strength is proportional to the density of the field lines ( # of lines is proportional to the mag. of the charge). 3. Electric Field is greatest between charges because the lines are closest there. Most field lines curve, especially away from the charges, but enter the charge surface perpendicularly.
ELECTRIC FIELD SHIELDING (Charges of a conductor) 1. Any access charges reside ON the surface of a conductor. Electrons experience forces of repulsion and on a conductor they are allowed to travel as far as they can which is toward the surface (the area that has the most space for them to spread out). 2. The electric field is zero at any point WITHIN a conducting material. The inside of the material is electrically neutral even with free electrons able to move under the influence of the field. 3. The conductor Shields any charge within it from electric fields created outside the conductor. Shielding results from the induced charges on the conducting surface. [This is particularly important and useful to shield electronic circuits from stray electric fields produced from various electrical appliances. This is why sensitive circuits in stereo amplifiers, TV s and computers are placed in metal boxes to protect them from fields produced by nearby hairdryers, blenders, irons and small appliances]. 4. The electric field just outside the surface of the conductor is perpendicular to the surface. This prevents there from being ANY component of the field parallel to the surface which would allow free electrons to move which would then not be electrostatic, but electron flow. 5. None of the above characteristics occur within an INSULATOR because they contain very few electrons that are free to move about.
Charges on and within a Conducting Sphere (or any shape) A cylindrical conductor with a cavity carved into it (basically this could be a hollow metal box) is placed in the electric field of a capacitor. The field lines induce a positive and negative charge to be induced on the surface of the shape on opposite sides. The field lines end and begin at these charges (like in a dipole where they only end at a charge. Therefore the field lines don t penetrate the sphere. The field lines enter the surface perpendicular to it, so no component of the field is parallel to the surface that would push charges along the surface (hence charges don t flow because it is electrostatic).
Electric Field Produced by a charge placed inside a hollow Conducting Sphere If a + charge is placed inside a conducting hollow sphere, the inside becomes negative and outside becomes positive and a field is produced that is the same as if it were produced from a + point charge. Therefore the hollow sphere doesn t shield the Outside from a field produced by a charge placed inside the sphere. However the field inside the hollow sphere is ZERO.
GAUSS LAW (Relationship between charge distribution and the field it produces) F E = E cosf A = q e 0 E cosf A is Electric Flux (F E ) E is the Electric field, A is the area of the surface the field falls on e 0 is Permittivity of free space (8.85 x 10-12 C 2 /N. m 2 ) f is the angle of the electric field with the normal to the Gaussian surface because only the perpendicular component of the field that passes through the surface is included in the flux.
Electric Field inside a Parallel Plate Capacitor The field inside the capacitor and away from the edges is constant (straight lines) and is : E = s/e 0 where s is charge density (q/a) 48. A rectangular surface (0.16m x 0.38m) is oriented in a uniform electric field of 580 N/C. What is the maximum possible electric flux through the surface? 50. A vertical wall (5.9m x 2.5m) in a house faces due east. A uniform electric field has a magnitude of 150 N/C. This field is parallel to the ground and points 35 o north of east. What is the electric flux through the wall?