( E ) = Lecture 1 Electric Charges & Coulomb s Law. Electric & Magnetic Fields. Electric Charge. Electric Charge

Transcription

1 Electric & Magnetic Fields Lecture 1 Electric Charges & Coulomb s Law Electric and magnetic fields manifest their existence through interactions with matter. Differential Form div E E = ( ) = div( B ) = B = 0 curl ( E ) = curl( B ) = ρ ε o E = B t Maxwell s Equations E B = µ o J ε o t Integral Form E da = Q enclosed B da = 0 ε o Lorentz Force F = qe qv B E d B l = t d A C B d l = E µ o I µ o ε o t d A C James Clerk Maxwell ( ) reducestatic-cling.html andreacarlisle.files.wordpress. com/01/0/staticcling_dogs.jpg Electric Charge Electric Charge Electric charge is an intrinsic characteristic of the fundamental particles that make up objects. Positive Charge Negative Charge Electrically neutral: object contains equal amounts of positive and negative charges Net charge: imbalance in charge Net charge of a system: algebraic sum of all the charges Law: Conservation of charge The net charge of a closed system never changes 1

2 Electric Charge Electric charge is quantized Elementary charge: q = ne, n = ±1,±, ±3,... e = (63) x C $ = n Business/images/us%0penny.jpg Coulomb (C): one coulomb is the amount of charge that is transferred through the cross section of a wire in 1 second when there is a current of 1 ampere in the wire. Charge of Particles Particles Charge Electron e Positron Proton Anti-Proton Neutron Photon 0 Up Quark 3 e Down Quark 1 Nucleus charge= Ze, atom with Z electrons is neutral. 3 e Proton charge: e = 1.60 x C Electron charge: e - = 1.60 x C e e e 0 Interaction of Charges Charged objects interact by exerting forces on one another. Conductors versus Insulators Conductors: material in which electric charges can move around freely. DEMO: Pith Balls Insulators: material in which electric charges are frozen in place. emi-conductor: material in which electric charges can move around but not as freely as in conductors. uper-conductor: no resistance to the movement of charge.

3 Interaction of Charges: Insulators Insulators: material in which electric charges are frozen in place. Interaction of Charges: Insulators Force of Repulsion Force of Attraction Charges with the same electrical sign repel each other Charges with opposite electrical signs attract each other. Mobility of Charge Conductors: material in which electric charges can move around freely. Mobility of Charge Demo: Pie Tins Negatively charged plastic rod will attract either end of the electrically isolated copper rod Reason: charges in copper rod can redistribute themselves. 3

4 Charging by Induction Charge Induction 1. Bring a charged rod close to conductor. 3. Break connection to ground, keeping the charged rod in place Demo: Chimes Charged Conducting thread. Ground the conductor. 4. Remove the rod. The sphere is charged. Insulating thread Grounded Coulomb s Law of Electro-static Force r q 1 q Charles-Augustin de Coulomb ( ) Coulomb s Law of Electro-static Force F = 1 Q 1 Q r ˆ 4πε o r The electro-static force of attraction/repulsion has a magnitude: where: F = k q 1 q r k = 1 4πε o = 8.99x10 9 Nm / C Coulomb s Law and the permittivity constant is ε o = 8.55x10 1 C / Nm 1 r Force repulsive F 1 Force by 1 on *Each particle exerts a force of this magnitude on the other particle. *The two forces form an action-reaction pair. r F 1 1 Force attractive - 4

5 Coulomb s Law of Electro-static Force Force exerted by q 1 on q at a distance r 1 F 1 = kq q 1 r 1, ˆr 1, q 1, q in coulombs (C) r 1 in meters (m) F 1 in newtons (N) F 1 ame sign charges: F 1 is in the direction of r 1,. Opposite sign charges: F 1 is in the direction opposite to r 1,. Coulomb s Law Analogous to Newton s Equation of Gravitation F = k q 1 q F = G m m 1 r r * k electro-static constant * Inverse quare Law * Charge *Attractive/repulsive depending on sign of charges *Two kinds of charges *Dominates on small scale Analogous DIFFER * G gravitational constant * Inverse quare Law * Mass *Always attractive *One kind of mass *Dominates on large scales Electro-tatic Force versus Newton s Force of Gravitational Attraction Problem olving trategies: DEMO: x 4 Draw a clear FORCE diagram Use consistent units (meter, Coulomb, Newton) Remember that the force is a vector Look for symmetry 5

6 Principle of uperposition When several point charges are put together, the total force on any one charge is the vector sum of the each of the separate forces acting on that charge. Exercise: y F 31 R=1m F Q 1 F 1 F = F 1y F 31y = F 1y F = k Q 1 Q r cos 30 0 N m F = F = N C (10 6 C) m ( ) Q 60 0 Determine force on Q 1 Q 3 Q 1 =Q =Q 3 =1µC x 6