Coulomb s Law & Electric Field Intensity

Transcription

1 Electromagnetic Fields and Waves Chinnawat, Ph.D. Coulomb s Law & Electric Field Intensity pop@alum.mit.edu L2-1 L2-2 Atoms Atom: smallest constituent unit of ordinary matter Atom = nucleus + surrounding electrons Nucleus = protons + neutrons Protons have a positive electric charge Electrons have a negative electric charge Neutrons have no electric charge Atoms must have equal numbers of protons and electrons An atom can gain or lose electrons, becoming an ion Atoms Atomic number: number of protons in an atom of an element Adding or removing protons from the nucleus of an atom creates a different element Mass Number = (Number of Protons) + (Number of Neutrons) Number of Protons = Atomic Number = 36 Number of Electrons = Number of Protons = Atomic Number = 36 Number of Neutrons = Mass Number - Atomic Number = = 48 L2-3 L2-4

2 Atoms Electrons of an atom are attracted to protons in an atomic nucleus by electromagnetic force Protons and neutrons in nucleus are attracted to each other by the nuclear force, usually stronger than the electromagnetic force repelling positively charged protons from one another Electron Charge = -e = x C Mass = x kg Proton Charge = +e = x C Mass = x kg L2-5 L2-6 Charge and Charge Density Charge and Charge Density Amber was rubbed with fur Rubbing supplied energy required for electrons to be removed Electrons were removed from the fur and deposited on the amber Amber became negatively charged and could attract small bits of material Electric charge causes forces in its vicinity Point charge Line charge density: Surface charge density: Volume charge density: L2-7 L2-8

3 Charge and Charge Density Ex: A charge is uniformly distributed over 3 structures such that a charge of Q = 10-9 C is distributed per unit length. Find charge density for each structure. (a) A very thin wire (b) A conducting wire of radius 10 mm. Assume charge can only exist on the surface of the wire. (c) A solid cylindrical, nonconducting material of radius 10 mm assuming the charge is uniformly distributed throughout the volume of the material Coulomb s Law Coulomb s law: an experimental law quantitatively defines force between 2 charges = dielectric constant or permittivity [C 2 /Nm 2 ] = [F/m] L2-9 L2-10 Coulomb s Law Ex: Charges Q 1 and Q 2 are located at (1,1,0) and (2,3,0) (a) Find force on Q 1 and Q 2 if Q 1 = 2 x 10-9 C and Q 2 = 4 x 10-9 C (b) Find force on Q 1 and Q 2 if Q 1 = 2 x 10-9 C and Q 2 = -4 x 10-9 C Sol: (a) (b) L2-11 L2-12

4 Coulomb s Law Electric Field Intensity View a fixed charge as a source of the force acting on the second charge Electric field intensity L2-13 L2-14 Electric Field Intensity Ex: An electron is located at a point in space. (a) Compute electric field intensity everywhere in space (b) Find force the electron exerts on a dust with a charge 3.2 x C and located at a distance R from the electron Sol: (a) Superposition of Electric Fields The field of a charge is unaffected by the existence of other charges or by the electric fields these charges generate (b) L2-15 L2-16

5 Electric Field Lines Superposition of Electric Fields Ex: Each 2 charges are connected with a very thin string to hold them in place. The string is designed to break when a force of 0.1 N is applied. (a) Calculate the charge Q require to break the string, if a = 20 mm. (b) What is the electric field intensity at the center of the string A-B? L2-17 L2-18 Superposition of Electric Fields Line Charge Distributions (a) (b) L2-19 L2-20

6 Line Charge Distributions Ex: A thin line segment is 2 m long and charged with a uniform line charge density ρ l. Find the electric field intensity at a distance a = 1 m from the center of the segment L2-21 L2-22 Line Charge Distributions Surface Charge Distributions L2-23 L2-24

7 Surface Charge Distributions Surface Charge Distributions Ex: A very thin plate of size 2a x 2b is charged with a uniform charge density ρ s. Calculate the electric field intensity parallel to the surface at the center of the plate. L2-25 L2-26 Volume Charge Distributions L2-27 L2-28

8 Electric Flux Density Electric flux density: independent of material properties Electric flux density of a point charge Q 1 at a distance R: L2-29