Electricity and Magnetism  Electric forces hold atoms and molecules together.  Electricity controls our thinking, feeling, muscles and metabolic processes.  Electricity and magnetism underpin much of our current technology (e.g. computers).  Electricity and magnetism are linked on a fundamental level.

Electric Charges Evidence for electric charges is everywhere, e.g. –static electricity. –lightning. Objects may become charged by contact and frictional forces. Benjamin Franklin (1700’s) discovered that there are two types of charges: –positive charge. –negative charge. Franklin also discovered that like charges repel and unlike charges attract one another. Electric charge is –quantized (Millikan) –conserved (Franklin)

Quantum of Electric Charge Electric charge is quantized. The smallest possible unit is the charge on one electron or one proton: e = ± x Coulombs No smaller charge has ever been detected in an experiment.

Electric Charges in Atoms Atoms consist of a nucleus containing positively charged protons. The nucleus of an atom is surrounded by an equal number of negatively charged electrons. The net charge on an atom is zero. An atom may gain or lose electrons, becoming an ion with a net negative or positive charge. Polar molecules have zero net charge but their charges are unevenly distributed in space (e.g. water). Nuclear diameter ~ m (femtometer) Atomic diameter ~ m (nanometer)

Classes of Materials CONDUCTORS are materials in which charges may move freely (e.g. copper). INSULATORS are materials in which charges cannot move freely (e.g. glass). SEMICONDUCTORS are materials in which charges may move under some conditions (e.g. silicon).

Charges and the Earth The earth acts as a near-infinite source or sink of charges, and therefore its net charge cannot easily be changed. Any conductor in contact with the earth is said to be GROUNDED and cannot receive a net charge. (principle of lightning rod)

Induced Charge Charged objects brought close to a conductor may cause charge to redistribute (polarize the conductor). If a polarized conductor is momentarily grounded, charge will be transferred to/from the earth, and it may be left with a net charge (by INDUCTION). Objects may be charged by –conduction (requires contact with another charged object. –induction (requires no contact with another charged object).

Electric Force and Coulomb’s Law If two point charges q 1 and q 2 are separated by a distance r, the magnitude of the electric force F e between them is: where k = 8.99 x 10 9 Nm 2 /C 2 is the Coulomb constant, q 1 and q 2 are in Coulombs ( C ), r is in meters ( m ) and F e is in Newtons ( N ).

Electric Force Vector The force on a point charge q 1 exerted by another point charge q 2 separated by a distance r 21 is:

Principle of Superposition For a system of N charges q 1, q 2, q 3, …, q N, the resultant force F 1 on q 1 exerted by charges q 2, q 3, …, q N is: Each charge may be considered to exert a force on q 1 that is independent of the other charges present.

Example #1 How many coulomb's of charge is contained in the electrons of one kg of hydrogen? One kg of hydrogen is 1000 grams, and has therefore 1000 times Avagadro's number of electrons. Q = 1000* N A * e where e = x C, and N A = Avogadro's number = 6.02 x Q = x 10 7 C

Example #2 Consider one gram of hydrogen gas which has been separated into its electrons and protons. The electrons are placed on Earth's north pole and the protons are placed on Earth's south pole. What is the magnitude of the force the electrons feel due to the presence of the protons? Remember that one gram of H gas has one mole (Avagadro's number) of hydrogen atoms. The force between the (+) and (-) charges is given by Coulomb's law where the separation distance r is 2*6.37E6 m. F = 5.14E5 N

Example #3 Two charges feel a repulsive force of 96 (N). What is the force if the separation, r, is quadrupled. Solution:

Example #4 Three charges are placed along a 10- mm line as shown in the diagram. Find the force felt by the proton if it is at the midpoint. Solution: 2eep

Example #5 Imagine 3 charges, separated in an equilateral triangle as shown above, with L = 2.0 cm, q = 1.0 nC. What is the magnitude and direction of the force felt by the upper charge? L

Example #5 (con’t) Solution: L

More Sample Problems Find the force experienced by the central charge. Where red dots represent an electron and green dots represents protons. The equilateral triangle below has sides of length 1fm. Find the force experienced by the central charge. Where red dots represent an electron and green dots represents protons. The sides of the square are1fm long.