Electric & Magnetic Fields

Transcription

1 Electric & Magnetic Fields Electric and magnetic fields manifest their existence through interactions with matter. Differential Form dive E div B B 0 o Maxwell s Equations Integral Form Q E da S S B da 0 enclosed o James Clerk Maxwell ( ) Lorentz Force F qe qv B curl E E B t C B E dl da t S E curl B B oj o t C E B dl I da t o o o S

2 Lecture 1 Electric Charges & Coulomb s Law ress.com/2012/02/staticcling_dogs.jpg

3 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

4 Electric 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

5 Electric Charge Electric charge is quantized $ = n q ne, n 1,2,3,... usiness/images/us%20penny.jpg Elementary charge: e = (63) x C 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.

6 Charge of Particles Particles Charge Electron Positron Proton Anti-Proton Neutron Photon Up Quark Down Quark Nucleus charge= +Ze, atom with Z electrons is neutral. Proton charge: e + = 1.60 x C Electron charge: e - = 1.60 x C e e e e e 1 3 e

7 Interaction of Charges Charged objects interact by exerting forces on one another. DEMO: Rod & Fur

8 Conductors versus Insulators Conductors: material in which electric charges can move around freely. Insulators: material in which electric charges are frozen in place. Semi-conductor: material in which electric charges can move around but not as freely as in conductors. Super-conductor: no resistance to the movement of charge.

9 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.

10 Mobility of Charge Conductors: material in which electric charges can move around freely. Negatively charged plastic rod will attract either end of the electrically isolated copper rod Reason: charges in copper rod can redistribute themselves.

11 Charging by Induction 1. Bring a charged rod close to conductor. 3. Break connection to ground, keeping the charged rod in place 2. Ground the conductor. 4. Remove the rod. The sphere is charged.

12 Interaction of Charges: Insulators Insulators: material in which electric charges are frozen in place.

13 Conductors versus Insulators Demo 5A-04: Charges are more readily transferred by conductors

14 Mobility of Charge Demo: Pie Tins

15 Charge Induction Demo: Chimes Charged Conducting thread Grounded Insulating thread

16 Coulomb s Law of Electro-static Force r q 1 q 2 Charles-Augustin de Coulomb ( ) The electro-static force of attraction/repulsion has a magnitude: where: F k q 1 q 2 r 2 k 1 4 o 8.99x10 9 Nm 2 / C 2 Coulomb s Law and the permittivity constant is o 8.55x10 12 C 2 / Nm 2

17 Coulomb s Law of Electro-static Force F 1 QQ 4 o r rˆ + 1 r + 2 Force repulsive F 12 Force by 1 on r F 12 Force attractive - 2 *Each particle exerts a force of this magnitude on the other particle. *The two forces form an action-reaction pair.

18 Coulomb s Law of Electro-static Force Force exerted by q 1 on q 2 at a distance r 12 F kq q 1 2rˆ ,2 r1,2 q 1, q 2 in coulombs (C) r 12 in meters (m) F 12 in newtons (N) F 12 Same sign charges: F is in the direction of r. 12 1,2 Opposite sign charges: F is in the direction opposite to r. 12 1,2

19 Problem Solving Strategies: Draw a clear FORCE diagram Use consistent units (meter, Coulomb, Newton) Remember that the force is a vector Look for (possible) symmetry

20 Principle of Superposition 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: F F 21y F 31y 2F 21y y F F 2 k Q 1 Q 2 r 2 cos 30 0 R=1m F 31 Q 1 F 21 F N m 2 F N C 2 (10 6 C) m 2 Q Determine force on Q 1 Q 3 Q 1 =Q 2 =Q 3 =1C x

21 Coulomb s Law Analogous to Newton s Equation of Gravitation F k q 1 q 2 F G m 1m 2 r 2 r 2 Analogous * k electro-static constant * Inverse Square Law * Charge * G gravitational constant * Inverse Square Law * Mass DIFFERS *Attractive/repulsive depending on sign of charges *Two kinds of charges *Dominates on small scale *Always attractive *One kind of mass *Dominates on large scales

22 Electro-Static Force versus Newton s Force of Gravitational Attraction F el k e r 2 2 F grav F el between the proton and the electron in a hydrogen atom in the ground state. From the Bohr model r=0.53 x m. F el F grav k G e 2 / r 2 m e m p / r kg 2 G m e r m C 2 ( C) 2 ( Kg)( Kg) 2 p F el F grav F el N F grav N Given such strong electrical interactions, atoms tend to remain uncharged. Matter prefers to be neutral. Forces we experience, if not gravitational, are electrical in nature (even though the net charge may be zero).

23 Electro-Static Force versus Newton s Force of Gravitational Attraction DEMO: 2 x 4