# Electromagnetism. Electricity Electromagnetism Magnetism Optics. In this course we are going to discuss the fundamental concepts of electromagnetism:

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1 Electromagnetism Electromagnetism is one of the fundamental forces in nature, and the the dominant force in a vast range of natural and technological phenomena The electromagnetic force is solely responsible for the structure of matter, organic, or inorganic Physics, chemistry, biology, materials science The operation of most technological devices is based on electromagnetic forces. From lights, motors, and batteries, to communication and broadcasting systems, as well as microelectronic devices. Engineering

2 Electromagnetism Electricity Electromagnetism Magnetism Optics In this course we are going to discuss the fundamental concepts of electromagnetism: charge force field potential current electric magnetic induction alternating waves circuit field currents reflection refraction image interference diffraction Once you master these basic concepts, you will be ready to move forward, into more advanced subjects in your specific field of interest

3 System of Units We will use the SI system SI International System of Units Fundamental Quantities Length meter [m] Mass kilogram [kg] Time second [s] Other Units Current ampere [A] Derived Quantities Force newton 1 N = 1 kg m / s 2 Energy joule 1 J = 1 N m Charge coulomb 1 C = 1 A s Electric Potential volt 1 V = 1 J / C Resistance ohm 1 Ω = 1 V / A

4 Electric Charges Forces and Fields Chapter 19

5 Electric Charge The Transfer of Charge SILK Glass Rod Some materials attract electrons more than others.

6 Electric Charge The Transfer of Charge + - SILK Glass Rod As the glass rod is rubbed against silk, electrons are pulled off the glass onto the silk.

7 Electric Charge The Transfer of Charge SILK Glass Rod Usually matter is charge neutral, because the number of electrons and protons are equal. But here the silk has an excess of electrons and the rod a deficit.

8 Electric Charge The Transfer of Charge SILK Glass Rod Glass and silk are insulators: charges stuck on them stay put.

9 Electric Charge The Transfer of Charge SILK Glass Rod Now the glass and the silk attract each other because they have opposite charges

10 Electric Charge + + Two positively charged rods repel each other. + Two rods with opposite charges attract each other.

11 Electric Charge History 600 BC Greeks first discover attractive properties of amber when rubbed AD Electric bodies repel as well as attract 1735 AD du Fay: Two distinct types of electricity 1750 AD Franklin: Positive and Negative Charge 1770 AD Coulomb: Inverse Square Law 1890 AD J.J. Thompson: Quantization of electric charge - Electron

12 Electric Charge Summary of things we know: There is a property of matter called electric charge. (In the SI system its units are Coulombs.) Charges can be negative (like electrons) or positive (like protons). In matter, the positive charges are stuck in place in the nuclei. Matter is negatively charged when extra electrons are added, and positively charged when electrons are removed. Like charges repel, unlike charges attract. Charges travel in conductors, not in insulators Force of attraction or repulsion ~ 1 / r 2

13 Crude representation of an atom showing positive charges (protons) inside the nucleus, and negative charges (electrons) orbiting around the nucleus. Conservation of Electric Charge The total electric charge in the universe is constant Objects get charged by exchange of charge with other objects (usually due to electron transfer from one object to another).

14 Most objects contains equal amounts of positive and negative charge, so they appear neutral on a macroscopic level Polarization When a charged rod is brought close to an object, in can distort the internal charges, giving rise to an attractive force between rod and object.

15 Uncharged amber rod exerts no force on scraps of paper (a) When the rod is rubbed against a piece of fur, it becomes charged by charge transfer (b) The charged rod attracts the scraps of paper by polarization (c)

16 Charge is Quantized q = multiple of an elementary charge e: e = 1.6 x Coulombs Charge Mass Diameter electron - e 1 0 proton +e 1836 ~10-15 m neutron ~10-15 m positron +e 1 0 (Protons and neutrons are made up of quarks, whose charge is quantized in multiples of e/3. Quarks can t be isolated.)

17 Insulators and Conductors In insulators, charges are not free to move long distances In metals, charges can move macroscopic distances Uncharged metal sphere touched by charged rod. Initially charged is transferred at the point of contact (a) Then, the charge spreads out (b) due to repulsion between like charges.

18 Coulomb s Law Coulomb s law describes the interaction between bodies due to their charges F = k q q 1 2 r 2 The direction of the force is along the line connecting the charges First calculate magnitude, then, determine direction F = F Notice: k = (4πε 0 ) -1 = 9.0 x 10 9 Nm 2 /C 2 ε 0 = permitivity of free space = 8.86 x C 2 /Nm 2

19 Gravitational and Electric Forces in the Hydrogen Atom M +e r 12 -e m m = kg M = kg r 12 = m Gravitational force Electric Force

20 Gravitational and Electric Forces in the Hydrogen Atom M +e r 12 -e m m = kg M = kg r 12 = m Gravitational force F g = G Mm r r 12 2 Electric Force F g = N

21 Gravitational and Electric Forces in the Hydrogen Atom M +e r 12 -e m m = kg M = kg r 12 = m Gravitational force F g = G Mm r r 12 2 Electric Force Fe = 1 πε Qq r r F g = N F e = N

22 Superposition of forces from two charges Blue charges are negative with equal charge (-q) What is the force on the positive red charge +q? y x NET FORCE

23 Superposition Principle F 13 F F 13 F 13y q 2 q 1 F 12 F 13x q 3 Forces add vectorially F 12y F 12 F = (F 12x + F 13x ) x + (F 12y + F 13y ) y F 12x

24 Example: electricity balancing gravity Two identical balls, with mass m and charge q, hang from similar strings of length l. θ l After equilibrium is reached, find the charge q as a function of θ and l q m q m

25 Example: electricity balancing gravity What forces are acting on the charged balls? θ l q m q m

26 Example: electricity balancing gravity Draw vector force diagram while identifying the forces. Apply Newton s 3 rd Law, for a system in equilibrium, to the components of the forces. Solve! F E T F G =mg T F G =mg F E

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