Review of EM Basics (from Phys1E03)

Lecture 2 Review of EM Basics (from Phys1E03) Sections: 2.1, 2.2, 8.1, 8.2, 8.5 Homework: See homework file LECTURE 2 slide 1

[istockphoto.com] ELECTRICITY LECTURE 2 slide 2

fundamental property of matter measured in coulombs (C) ampere (A) is a basic unit in SI and coulomb is a secondary unit derived from it more on the minus sign later Electric Charge 1 dq i = C=A s dt i is the electric current in amperes (A) Q is the electric charge in coulombs (C) t is time in seconds (s) LECTURE 2 slide 3

charged particles in atoms: electrons and protons these particles react in opposite way to the influence of external electric fields they have opposite charges convention is that protons have positive charge, and electrons have negative charge electron charge is equal in magnitude to the charge of a proton electron charge is the smallest indivisible amount of charge Qe Electric Charge we are concerned with macroscopic charges, i.e., charge distributions much larger than the dimensions of the largest atomic nucleus ( 10-15 m) 19 = e 1.60217662 10, C LECTURE 2 slide 4

Field of Point Charge the point charge features spherical symmetry, which implies the spherical symmetry of its field F e equipotential lines and force lines of a point charge http://www.falstad.com/vector3de/fullscreen.html http://www.falstad.com/mathphysics.html ϕ = const LECTURE 2 slide 5

Coulomb s Law (1785) 1 QQ 1 2 F2 = a 2 12 = F1, N 4 πε R12 k Charges of the same sign repel each other; charges of the opposite signs attract each other. the inverse square law is a universal property of all 3D static fields LECTURE 2 slide 6

TRUE OR FALSE? Two charges Q 1 and Q 2 are 8 cm apart. The force 12 acting on Q 2 is F2 = ay9 10, N. Q1: If we set the charges 24 cm apart, the force will become F 12 2 = ay3 10, N. Q2: If we replace Q 1 with Q 3 = Q 1 /3, the force will become F 12 2 = ay3 10, N. LECTURE 2 slide 7

Coulomb s Law 2 the constant of proportionality k depends on the system of units. In SI, k = 1/(4 πε ) 2 2 N m N m V m k = = C A s [ ] = = 2 2 2 C in vacuum, if the force is measured in newtons, the distance in meters, and the charge in ampere-seconds (coulombs): 9 k0 9.0 10 theoretically, this constant in the SI system must be exactly 7 2 k0 = 10 c where c is the speed of light Coulomb Forces and Flame: https://www.youtube.com/watch?v=a7_8gc_llr8 m? LECTURE 2 slide 8

Dielectric Permittivity in Coulomb s Law the constant 1 ε = 4π k is called dielectric permittivity, which in vacuum is 9 1 1 10 ε0 = = F/m 2 7 9 4πc 10 4π 9 10 36π a more precise value is 12 ε0 8. 854187817 10, F/m = C/(V m) LECTURE 2 slide 9

electric field vector the force exerted on a unit charge E = Electric Field (Intensity) Vector lim Q 0 F, N/C=V/m Q F=QE, N Q is a test (probe) charge, the value and size of which are small enough not to disturb the measured original field of the source electric field of a positive point charge located at the origin of a spherical coordinate system E = 1 Q 2 4πε r a r, V/m LECTURE 2 slide 10

Electric Field: Example What is the minimum E-field necessary to counteract the gravitational pull on an electron on Earth? LECTURE 2 slide 11

Dielectric Permittivity in Coulomb s Law the dielectric permittivity of materials is usually different from that of vacuum due to polarization it is usually given relative to that of vacuum via the relative dielectric permittivity (dielectric constant) ε r ε= εε some examples of relative permittivity values Air: εr 1.0006 Water: εr 80 Urban (dry) ground: εr 3 Rural (moist) ground: εr 14 r 0 LECTURE 2 slide 12

Dielectric Permittivity: Example [Serway&Jewett, Physics for Scientists and Engineers] Why does the capacitance of a capacitor increase ϵ r times when a dielectric of relative permittivity ϵ r is inserted between the two electrodes? LECTURE 2 slide 13

Dielectric Permittivity: Example 2 E ext dielectric LECTURE 2 slide 14

[askiitians.com] MAGNETISM LECTURE 2 slide 15

Magnets as Sources of Static Magnetic Field bar magnet [thoughtco.com] U (horseshoe) magnet [shutterstock.com] a magnet has two poles: North (positive) and South (negative) like poles repulse; opposite poles attract Can you obtain a magnet with one pole only, e.g., North pole only? [slideplayer.com] LECTURE 2 slide 16

Magnetic Forces Review Ampère s Force Law S Ampère s force law (aka motor equation) F = IL( a B), N m I magnetic flux density vector (the magnetic field force vector) video on wire with current in magnet http://www.fyzikalni-experimenty.cz/en/electromagnetism/threadwith-current-in-a-magnetic-field/ force does not depend on position if I = const. and B = const. (expected for a large flat field source) You want to increase the magnetic force F m on the wire 10 times while still using the same magnet. How would you propose to achieve that? N N LECTURE 2 slide 17 I B Fm S L

Ampère s Force Law: Example Magnetic field B = 0.5a z T is due to a magnet with flat poles. What is the force exerted on a piece of wire with current I = 2 A of length L = 10 cm and orientation given by the unit vector ( ) a = 1a 1 a / 2 L y z LECTURE 2 slide 18

Magnetic Forces Review Lorentz Force Law Lorentz force law follows directly from Ampère s force law for a very short current element I L (B is locally constant) Fm = I( L B), N Q I = L Q t L = v Fm = Q( v B), N A m for a single charge carrier of charge Q charge that fills up volume s L in time t s e e e e e e e e L Q = v t I V F = Qv B, N (holds for point charge Q) m LECTURE 2 slide 19

Lorentz Force Law: Example An electron (Q e 1.602 10 19 C) is moving in a piece of metal with drift velocity v d = 3.2 m/s due to electric field E = 1 kv/m. Magnetic field B = 1.2 T is orthogonal to the wire. Find the electric and magnetic forces exerted on the electron. LECTURE 2 slide 20

Lorentz Force Law: Homopolar Motor [http://www.fyzikalni-experimenty.cz/en/electromagnetism/] 1) Homopolar motor with a nail 2) Homopolar motor with wire https://www.youtube.com/watch?v=zodboryf1hm LECTURE 2 slide 21

We have reviewed Coulomb's law for the force between two point charges the E-vector as the electric force per unit charge the E-vector of a point charge the impact of relative permittivity on capacitance of capacitors the magnetic field of magnets Ampère s force law (the motor equation) the Lorentz force LECTURE 2 slide 22