* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Electric Charges, Forces and Fields
Survey
Document related concepts
History of subatomic physics wikipedia , lookup
Nuclear physics wikipedia , lookup
Elementary particle wikipedia , lookup
Condensed matter physics wikipedia , lookup
Introduction to gauge theory wikipedia , lookup
Anti-gravity wikipedia , lookup
Electrical resistivity and conductivity wikipedia , lookup
Time in physics wikipedia , lookup
History of electromagnetic theory wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Fundamental interaction wikipedia , lookup
Chien-Shiung Wu wikipedia , lookup
Maxwell's equations wikipedia , lookup
Field (physics) wikipedia , lookup
Lorentz force wikipedia , lookup
Electromagnetism wikipedia , lookup
Transcript
Physics 202 Professor P. Q. Hung 311B, Physics Building Physics 202 – p. 1/2 Electric Charges, Forces and Fields http://galileo.phys.virginia.edu/~pqh/202/PHYS_ 202_ homepage.htm Physics 202 – p. 2/2 Electric Charges, Forces and Fields http://galileo.phys.virginia.edu/~pqh/202/PHYS_ 202_ homepage.htm Important informations contained in the homepage. Physics 202 – p. 2/2 Electric Charges, Forces and Fields A problem: 3 charges lie along the x-axis. Charge q1 = 1µC is at the origin. Charge q2 = −3µC is at x = −0.30m. Charge q3 = −4µC is at x = +0.20m. Find the net electrostatic force acting on q1 . Physics 202 – p. 3/2 Electric Charges, Forces and Fields A problem: 3 charges lie along the x-axis. Charge q1 = 1µC is at the origin. Charge q2 = −3µC is at x = −0.30m. Charge q3 = −4µC is at x = +0.20m. Find the net electrostatic force acting on q1 . What is an electric charge? What is this strange unit µC? What is the meaning of an electrostatic force on one charge in the presence of two other charges? Is it a contact force or not? Physics 202 – p. 3/2 Electric Charges, Forces and Fields Electric charges Electricity comes from the Greek elektron = Amber. Physics 202 – p. 4/2 Electric Charges, Forces and Fields Electric charges Electricity comes from the Greek elektron = Amber. Rub an amber rod and you can pick up little pieces of papers, a phenomenon usually referred to as “static electricity”. ⇒ The rod becomes “charged” by rubbing. Physics 202 – p. 4/2 Electric Charges, Forces and Fields Electric charges Electricity comes from the Greek elektron = Amber. Rub an amber rod and you can pick up little pieces of papers, a phenomenon usually referred to as “static electricity”. ⇒ The rod becomes “charged” by rubbing. You rub two amber rods and put them close to each other: They repel each other. Physics 202 – p. 4/2 Electric Charges, Forces and Fields Electric charges Electricity comes from the Greek elektron = Amber. Rub an amber rod and you can pick up little pieces of papers, a phenomenon usually referred to as “static electricity”. ⇒ The rod becomes “charged” by rubbing. You rub two amber rods and put them close to each other: They repel each other. You rub two glass rods and put them close to each other: They repel each other. Physics 202 – p. 4/2 Electric Charges, Forces and Fields Electric charges You rub one amber rod and one glass rod and put them close to each other: They attract each other. ⇒ Two kinds of charges! Physics 202 – p. 5/2 Electric Charges, Forces and Fields Electric charges You rub one amber rod and one glass rod and put them close to each other: They attract each other. ⇒ Two kinds of charges! Like charges repel while unlike charges attract. Physics 202 – p. 5/2 Electric Charges, Forces and Fields Electric charges You rub one amber rod and one glass rod and put them close to each other: They attract each other. ⇒ Two kinds of charges! Like charges repel while unlike charges attract. Benjamin Franklin: positive charge for the rubbed glass rod and negative charge for the rubbed amber rod. Arbitrary choice! Physics 202 – p. 5/2 Electric Charges, Forces and Fields Electric charges Electric charge is conserved! If some positive amount of charges is produced somewhere, an equal amount of negative charge is also produced. Physics 202 – p. 6/2 Electric Charges, Forces and Fields Electric charges Electric charge is conserved! If some positive amount of charges is produced somewhere, an equal amount of negative charge is also produced. The unit of charge is C which stands for Coulomb. Physics 202 – p. 6/2 Electric Charges, Forces and Fields Electric charges Electric charge is conserved! If some positive amount of charges is produced somewhere, an equal amount of negative charge is also produced. The unit of charge is C which stands for Coulomb. Where do these charges come from? From the atom! Physics 202 – p. 6/2 Electric Charges, Forces and Fields Electric charges: The Atom Physics 202 – p. 7/2 Electric Charges, Forces and Fields Electric charges Atom: object with a nucleus (made out of protons and neutrons) carrying a net positive charge surrounded by electrons carrying a net negative charge of the same magnitude. Atoms are neutral. Physics 202 – p. 8/2 Electric Charges, Forces and Fields Electric charges Atom: object with a nucleus (made out of protons and neutrons) carrying a net positive charge surrounded by electrons carrying a net negative charge of the same magnitude. Atoms are neutral. The charge of the proton is +|e| = 1.6 × 10−19 C and that of the electron is −|e| = −1.6 × 10−19 C. That of the neutron is zero. A neutral atom has an equal number of protons and electrons. Physics 202 – p. 8/2 Electric Charges, Forces and Fields Electric charges Charges can be exchanged by removing or adding electrons. Physics 202 – p. 9/2 Electric Charges, Forces and Fields Electric charges Charges can be exchanged by removing or adding electrons. A neutral atom with electrons removed ⇒ a positive ion; added ⇒ a negative ion. Physics 202 – p. 9/2 Electric Charges, Forces and Fields Electric charges Charges can be exchanged by removing or adding electrons. A neutral atom with electrons removed ⇒ a positive ion; added ⇒ a negative ion. Nucleus: positively-charged protons + electrically neutral particles: neutrons. Modern theory of particle physics: protons and neutrons are made out of even smaller, electrically charged particles: the quarks. We are all made out of charged particles! Physics 202 – p. 9/2 Electric Charges, Forces and Fields How does a charged rod attract a neutral piece of paper? Physics 202 – p. 10/2 Electric Charges, Forces and Fields Insulators and Conductors Materials with electrons loosely bound to the nuclei and which can “freely” move within ⇒ conductor. “Free” electrons: conduction electrons. Examples are metals. Physics 202 – p. 11/2 Electric Charges, Forces and Fields Insulators and Conductors Materials with electrons loosely bound to the nuclei and which can “freely” move within ⇒ conductor. “Free” electrons: conduction electrons. Examples are metals. Materials with electrons very tightly bound to the nuclei and which cannot freely move about: insulators. Wood is an example. Physics 202 – p. 11/2 Electric Charges, Forces and Fields Insulators and Conductors Materials with electrons loosely bound to the nuclei and which can “freely” move within ⇒ conductor. “Free” electrons: conduction electrons. Examples are metals. Materials with electrons very tightly bound to the nuclei and which cannot freely move about: insulators. Wood is an example. In between, materials with few conduction electrons and which have interesting properties: semiconductors. Silicon is an example. Physics 202 – p. 11/2 Electric Charges, Forces and Fields Charging a Conductor Physics 202 – p. 12/2 Electric Charges, Forces and Fields Coulomb’s Law Recall the attractive gravitational force between two masses, m1 and m2 : Fg = m1 m2 −G r2 Physics 202 – p. 13/2 Electric Charges, Forces and Fields Coulomb’s Law Recall the attractive gravitational force between two masses, m1 and m2 : Fg = m1 m2 −G r2 Experimental discovery by Coulomb: Coulomb’s Law. Electrostatic force between two point charges, q1 and q2 : Fe = q1 q2 k r2 2 (1) k = 8.99 × 109 N.m2 /C . (1) is valid not just for point charges but also for charge distributions Physics 202 – p. 13/2 Electric Charges, Forces and Fields Gravitational force vs Electrostatic force The gravitational force is always attractive while the electrostatic force can be attractive or repulsive depending on the sign of the product q1 q2 . Physics 202 – p. 14/2 Electric Charges, Forces and Fields Gravitational force vs Electrostatic force The gravitational force is always attractive while the electrostatic force can be attractive or repulsive depending on the sign of the product q1 q2 . The electrostatic force is attractive when q1 q2 < 0, i.e. the two charges have opposite signs (one positive and the other one negative). Fe = |q1 | |q2 | −k r2 (1) Physics 202 – p. 14/2 Electric Charges, Forces and Fields Gravitational force vs Electrostatic force The electrostatic force is repulsive when q1 q2 > 0, i.e. the two charges have the same signs (either both positive or both negative). Fe = |q1 | |q2 | k r2 (1) Physics 202 – p. 15/2 Electric Charges, Forces and Fields Gravitational force vs Electrostatic force The electrostatic force is repulsive when q1 q2 > 0, i.e. the two charges have the same signs (either both positive or both negative). Fe = |q1 | |q2 | k r2 2 (1) Since Fe goes like 1/r , the electrostatic force becomes stronger for smaller distances and vice versa. Strong bonding at short distances for objects such as adhesive tapes. Physics 202 – p. 15/2 Electric Charges, Forces and Fields Coulomb’s Force is a vector F~21 = k q1r2q2 r̂ where r̂ = ~r/r is the unit vector pointing from q1 to q2 . F~21 : Force on q2 due to q1 . Physics 202 – p. 16/2 Electric Charges, Forces and Fields Some examples Physics 202 – p. 17/2 Electric Charges, Forces and Fields A problem 3 charges lie along the x-axis. Charge q1 = 1µC is at the origin. Charge q2 = −3µC is at x = −0.30m. Charge q3 = −4µC is at x = +0.20m. Find the net electrostatic force acting on q1 . Concept: Net force on q1 = Vector sum of the electrostatic forces on q1 due to q2 and q3 ⇒ Superposition Principle. Physics 202 – p. 18/2 Electric Charges, Forces and Fields A problem 3 charges lie along the x-axis. Charge q1 = 1µC is at the origin. Charge q2 = −3µC is at x = −0.30m. Charge q3 = −4µC is at x = +0.20m. Find the net electrostatic force acting on q1 . Concept: Net force on q1 = Vector sum of the electrostatic forces on q1 due to q2 and q3 ⇒ Superposition Principle. Draw a picture of the forces Physics 202 – p. 18/2 Electric Charges, Forces and Fields A problem: Solution q1 q2 = −3(µC)2 = −3 × 10−12 C 2 is negative. The force on q1 from q2 is attractive and points in the negative x-direction (toward q2 ). Let the unit vector pointing in the positive x-direction be î. One obtains 9 2 2 3×10−12 C 2 ~ F12 = −(8.99 × 10 N.m /C ) (0.30m)2 î = −0.30 N î. Physics 202 – p. 19/2 Electric Charges, Forces and Fields A problem: Solution Similarly, q1 q3 = −4(µC)2 = −4 × 10−12 C 2 is negative. The force on q1 from q3 is attractive and points in the positive x-direction (toward q3 ). One obtains 9 2 2 4×10−12 C 2 ~ F13 = (8.99×10 N.m /C ) (0.20m)2 î = 0.90 N î. Physics 202 – p. 20/2 Electric Charges, Forces and Fields A problem: Solution The net force on q1 is F~net = F~12 + F~13 = 0.60 N î and points in the positive x-direction. Physics 202 – p. 21/2 Electric Charges, Forces and Fields A problem: Solution The net force on q1 is F~net = F~12 + F~13 = 0.60 N î and points in the positive x-direction. Summary: 1) Calculate each force separately; 2) Sum the 2 forces as vectors to get the final result. Physics 202 – p. 21/2 Electric Charges, Forces and Fields Coulomb’s Law: Charge distributions Coulomb’s law also applies to charge distribution: Same formula. Physics 202 – p. 22/2 Electric Charges, Forces and Fields Coulomb’s Law: Charge distributions Coulomb’s law also applies to charge distribution: Same formula. Example: Charge distributed uniformly over the volume of a sphere of radius R with a volume charge density ρ ⇒ Total charge Q = ρ( 43 πR3 ). Physics 202 – p. 22/2 Electric Charges, Forces and Fields Coulomb’s Law: Charge distributions Coulomb’s law also applies to charge distribution: Same formula. Example: Charge distributed uniformly over the volume of a sphere of radius R with a volume charge density ρ ⇒ Total charge Q = ρ( 43 πR3 ). Electrostatic force between 2 such spheres: F~e = k Q1r2Q2 r̂ Physics 202 – p. 22/2 Electric Charges, Forces and Fields Electric field Recall: F~21 = k q1r2q2 r̂ (1) Physics 202 – p. 23/2 Electric Charges, Forces and Fields Electric field Recall: F~21 = k q1r2q2 r̂ (1) Define an electric field due to q1 : ~ E(r) = k q12 r̂ r Physics 202 – p. 23/2 Electric Charges, Forces and Fields Electric field Recall: F~21 = k q1r2q2 r̂ (1) Define an electric field due to q1 : ~ E(r) = k q12 r̂ r Rewrite (1) as ~ (1) F~21 = q2 E(r) Physics 202 – p. 23/2 Electric Charges, Forces and Fields Electric field Recall: F~21 = k q1r2q2 r̂ (1) Define an electric field due to q1 : ~ E(r) = k q12 r̂ r Rewrite (1) as ~ (1) F~21 = q2 E(r) This is the force on q2 in the presence of an ~ electric field E(r) Physics 202 – p. 23/2 Electric Charges, Forces and Fields q ~ Electric field of point charge: E(r) = k r2 r̂ Physics 202 – p. 24/2 Electric Charges, Forces and Fields Electric field: Example problem Two positive point charges, q1 = +16µC and q2 = +4µC, are separated in a vacuum by a distance of 3.0m. Find the spot on the line between the two charges where the net electric field is zero. The electric field is a vector. Physics 202 – p. 25/2 Electric Charges, Forces and Fields Electric field: Example problem Two positive point charges, q1 = +16µC and q2 = +4µC, are separated in a vacuum by a distance of 3.0m. Find the spot on the line between the two charges where the net electric field is zero. The electric field is a vector. The net electric field is the vector sum of the two individual electric fields. Physics 202 – p. 25/2 Electric Charges, Forces and Fields Electric field: Example problem Since both charges are positive, the electric fields coming from q1 and q2 at any point in between will be pointing in the opposite direction to each other. Therefore the net electric field will be the difference of the two individual electric fields. Physics 202 – p. 26/2 Electric Charges, Forces and Fields Electric field: Example problem Let l be the distance from q1 of the point in between where the two electric fields exactly cancel each other, resulting in a zero net electric field. One has 4µC k 16µC = k l2 (3.0m−l)2 4.0(3.0m − l)2 = l2 2.0(3.0m − l) = ±l l = 2.0m; l = 6.0m Only l = 2.0m is the correct answer (in between point). Physics 202 – p. 27/2