Electric charge is a fundamental property of matter that exists in two forms: positive or negative. Like charges repel and unlike charges attract. Charge is quantized and conserved within isolated systems. Conductors readily transmit charges through loosely bound outer electrons, while insulators do not transmit charges at all. Charged objects create electric fields that exert forces on other charges according to Coulomb's law. The electric field is defined as the force felt by a test charge placed at a given point. Field lines depict the direction and strength of the electric field. Within conductors, the electric field is zero and excess charge resides entirely on the surface. The field is strongest at sharp points on conductors.

1. Electric Charge, Forces, and Fields

2. Electric Charge We already know: Electric charge is a fundamental property of matter There are two electric charges: positive or negative (arbitrarily named) The atom consists of a small positive nucleus surrounded by a negative electron cloud

3. Electric Charge Like charges repel; unlike charges attract. As with Mass/Energy: Charge is conserved The net charge of an isolated system remains constant. This is another fundamental law in physics

4. Electric Charge SI unit of charge: the coulomb, C. All charges in nature are integer multiples of the charge on the electron:

5. Conductors Most atoms hold on to their electrons tightly and are insulators. In aluminum, the valence electrons are essentially free and strongly repel each other. Any external influence which moves one of them will cause a repulsion of other electrons which propagates, "domino fashion" through the conductor. In a conducting material, the outer electrons of the atoms are loosely bound and free to move through the material.

7. Electrostatic Charging Objects can have excess charge of one polarity or another. An electroscope may be used to determine if an object is electrically charged.

8. Electrostatic Charging An electroscope can be given a net charge by conduction – when it is touched with a charged object, the excess charges flow freely onto the electroscope.

9. Electric Force The force exerted by one charged particle on another is given by:

10. Electric Force If there are multiple charges, the force vectors must be added to get the net force on another charge. We can say that charges produce an “electric field” (and similarly, masses produce a “gravitational field”). The field describes the force felt by a test charge if it were placed into the field

11. Electric Field Definition of the electric field: force on a charge if there were a charge The direction of the field is the direction the force would be on a positive charge. 

12. Electric Field Charges create electric fields, and these fields in turn exert electric forces on other charges. Electric field of a point charge: (Pointing away from the charge)

13. Electric Field For multiple charges, the total electric field is found using the superposition principle: For a configuration of charges, the total, or net, electric field at any point is the vector sum of the electric fields due to the individual charges.

14. Electric Field Example: electric field from three point charges Three point charges are located on a circular arc as shown in the figure below. (Take r = 3 cm. Let to the right be the + x direction and up along the screen be the + y direction.) Answer: from symmetry, E has no y-component, the x component is given by: = same field as if a single charge with +1 nC was located at the point where the negative charge is

16. Electric Field: examples Electric field lines of a dipole: A dipole is an arrangement of charge with positive charge on one end and negative charge on the other. From far away, the dipole is “invisible”, i.e. it looks neutral. Close to the dipole, the electric field looks as drawn on the left.

17. Electric Field: examples Electric field lines of a dipole: Threads in oil with two charged spheres: threads have electric dipole and so line up with field, can “see” electric fierd lines

18. Electric Field: examples Electric field lines due to very large parallel plates: Superposition: fields not normal to surface cancel

20. Electric Field Often, tricks and symmetry considerations can help us find electric fields in a problem. Consider equal 8 charges arranged equally spaced around a circle: What’s E-field at P, center of the circle? What if we take one charge away? Taking one charge away is the same as adding a negative charge to that position. Superposition principle says the E-field is the same as the field coming from one negative charge

21. Conductors and Electric Fields Electric charges are free to move within a conductor; therefore, there cannot be a static field within the conductor: 1) The electric field is zero inside a conductor Excess charges on a conductor will repel each other, and will wind up being as far apart as possible. 2) Any excess charge on a conductor resides entirely on the surface of the conductor There cannot be any component of the electric field parallel to the surface of a conductor; otherwise charges would move. 3) The electric field at the surface of a charged conductor is perpendicular to the surface

22. Conductors and Electric Fields

23. Conductors and Electric Fields The force from neighboring charges is less when the curvature of the surface is large: Excess charge tends to accumulate at sharp points, or locations of highest curvature, on charged conductors. As a result, the electric field is greatest at such locations.

24. Conductors and Electric Fields Electric field is strongest near sharp points: That is why lightning rods have sharp points, and why lightning strikes buildings with sharp points. Lightning happens when an electric field in the Earths atmosphere becomes so large that electrons are ripped off of atoms in the air