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PHYSICS 112 Dr. Anatoli Frishman [email protected] Physics Mechanics Thermal properties Electromagnetism •Electrostatic •Electric current •Magnetism Condensed Mater High energy Optics Atoms & particles •Geometrical optics •Wave optics Biophysics Classical physics Quantum physics Relativistic physics Quantum relativistic physics Electromagnetism (electric and magnetic phenomena) This is about: electric charges, electromagnetic forces, and electromagnetic fields I. Electrostatics This is about: non-moving electric charges, electrostatic forces, and electrostatic fields. (With very good approximation, electrostatics could be applied to slow moving charges. Slow means that the speed of the considered charge is much smaller then speed of light: v<<c) 1. Electric charge 1a. Qualitative description •There are two and only two types of electric charges •Charges of the same type repel, and charges of different type attract (this is already qualitative description of electrostatic forces) •These two types are referred to as positive and negative (+q and –q) •Charges can be treated algebraically, and the net amount of electric charges in an isolated system is conserved (is not changed in any process). This is the law of conservation of electric charges 1b. Elementary charge: e 1.6 10 19 C 1c. Electric properties of different materials (very brief, qualitative description) •Microscopic picture (atom) •Insulators •Conductors •Semiconductors •Superconductors 1d. “Games” with electric charges •Charging by contact •Charging by induction •Electroscope •Electrometer The electroscope disk Positive Negative Neutral Gold leaves (or vane) Charged rod Positive Inducted charge Negative Neutral Inducted charge repulsion Charged rod (closer) Positive Negative Neutral Stronger repulsion If we ground the electroscope while the rod is there, the charges in the electroscope that were “escaping” from the rod flow to the ground. Positive Negative Neutral No repulsion Then we cut the grounding… Positive Negative Neutral No repulsion And remove the rod… The electroscope is now charged. The charge spreads now all over the object. Electroscope charged by induction Positive Negative Neutral Repulsion 2. Electrostatic forces (Coulomb’s law) F k k 1 40 Q1Q2 r2 Q1 8.99 109 Nm 2 / C 2 Units: r Q2 0 permittivi ty constant Q I Q It t [Q ] 1C 1A 1s [ I ] 1A Example: Q1 2.0 10 6 C Q2 3.0 10 6 C r 0.10m F ? F 9.0 109 Nm2 / C 2 F 5.4 N 2.0 10 6 C 3.0 10 6 C 0.1m2 Coulomb’s law in vector form: F12 Q1 r Q2 Q1 and Q2 have the same sign Q1Q2 >0 Principle of superposition: Q1Q2 r12 F12 F21 k 2 r r F21 Q1 F12 r F21 Q2 Q1 and Q2 have opposite signs Q1Q2 <0 Fnet F1 F2 ... Example: Q1 1.0 C Q1 F12 Q2 2.0 C r F13 Q2 F1 F12 F13 Q3 r F1 F12 F13 Q3 12.0 C r 0.10m F1 ? F12 k Q1Q2 F13 k Q1Q3 r 2 2r 2 9.0 10 9 Nm 2 / C 2 9.0 10 9 Nm 2 / C 2 1.0 10 6 C 2.0 10 6 C 0.1m 2 1.0 10 6 C 12.0 10 6 C 2 0.1m F1 F12 F13 1.8 N 2.7 N 0.9 N F1 k Q1Q2 r 2 k Q1Q3 2r 9.0 10 Nm / C 9 2 2 2 k Q1 r 2 1.0 10 6 C 0.1m2 Q2 Q3 4 12.0 10 6 C 2.0 10 C 0.9 N 4 6 2 1.8 N 2.7 N Q Example: Q 1.0 C a 0.10m F ? Ftot Q a Q Q F2 2 F1 F3 F3 Q2 F1 F2 k 2 a Q2 F3 k 2 2a Ftot F1 F2 F3 F1 Q2 Q2 1 Q2 2k 2 k 2 k 2 2 a 2a 2 a 1 1.0 10 C Ftot 2 8.99 109 Nm 2 / C 2 2 0.10m 2 -6 2 1.7 N Example: Compare the gravitational attraction and the electric repulsion of two electrons e 1.6 1019 C e2 FE k 2 r m 9.1 10 31 kg m2 FG G 2 r 19 2 FE 9.0 10 Nm C 1.6 10 C ke 2 FG Gm 6.7 10 11 Nm 2 kg 2 9.1 10 31 kg 2 9 2 2 2 4.2 10 42 Big! Example: One of your friends can resist a force of 100 lb (450 N) with his arms apart. You give him two charged balls with charges Q and Q to hold on each hand. How large a charge Q can he hold outstretched? Q2 F k 2 r Qmax Q -Q r ~ 1.5 m r2 Fmax 3.35 10 4 C ke -31 9.1 10 kg 1 electron -15 3.35 104 C 2 10 kg -19 1.6 10 C 1 electron Less than a cell in your body!