Fundamentals of Engineering Exam Review Electromagnetic Physics

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1 Dr. Gregory J. Mazzaro Spring 2018 Fundamentals of Engineering Exam Review Electromagnetic Physics (currently 5-7% of FE exam) THE CITADEL, THE MILITARY COLLEGE OF SOUTH CAROLINA 171 Moultrie Street, Charleston, SC 29409

2 FE Exam Subjects 2

3 Charge vs. Current charge is the basic unity of electricity (a property of protons & electrons) particles that attract each other (opposite charge ) or repel each other (same charge ) as EEs, we focus on the behavior of electrons fundamental unit of charge (SI system) = coulomb 1 electron holds a charge of q = x C 1 proton holds a charge of q = x C current = the flow of charge unit of current = ampere 1 ampere = 1 C / s (1 coulomb flowing past a point per second, usually within a wire) 3

field (E) is the force that a unit charge experiences (N/C) due to the

4 Electric Field & Coulomb s Law a field is a vector (with magnitude & direction) defined at all points in space, (x, y, z) Q 2 r a r12 an electric field (E) is the force that a unit charge experiences (N/C) due to the presence of other charges nearby governed by Coulomb s Law Q 1 E field vectors D flux lines 4

5 Example: Electric Field (A) mn, away from the 2-nC charges (B) mn, away from the 2-nC charges (C) mn, towards the 2-nC charges (D) mn, towards the 2-nC charges The correct answer is (A). 5

6 Example: Electric Field & Potential V F QE Q The correct answer is (B). d 6

electric field intensity ds is normal to the surface and directed outward

7 Gauss Law -- 1 of Maxwell s Equations which governs the behavior of electric fields Q encl = charge contained in a Gaussian surface E = electric field intensity ds is normal to the surface and directed outward (sphere) an alternative to Coulomb s Law for determining electric field, under symmetry 7

8 Example: Gauss Law 8

9 Example: Gauss Law 9

energy is dissipated (as heat) r = resistivity, a material

10 Resistivity All real wires have a non-zero resistance. when current flows along a non-zero resistance, voltage drops and energy is dissipated (as heat) r = resistivity, a material property (W-m) L Also, real materials become more current-resistant as they heat up. 10

11 Example: Resistivity The correct answer is (C). 11 R r 2 P I R L A I J I J A A P 2 R 2 r I J A L L A J A r W

12 Capacitance & Stored Energy A capacitor is a linear circuit element which stores energy in the electric field in the space between two conducting bodies occupied by a material with permittivity e. 12

13 Example: Capacitance 13

14 Example: Electrostatic Energy 2 Qd 2 Q V E e A e A

charge = voltage unit of voltage = volt = 1 J/C can exist even when no

15 Voltage / Potential / Work energy must be expended to move charge work required to move charge through an element or through a field, per charge = voltage unit of voltage = volt = 1 J/C can exist even when no current is flowing potential Circuit theory Electromagnetic theory QV 15

16 Example: Electromagnetic Work 16

17 Magnetic Fields 17

18 Inductance & Stored Energy An inductor is a linear circuit element which stores energy in the magnetic field in the space between current-carrying wires occupied by a material with permeability m. 18

19 Example: Magnetostatic Energy 19

20 Example: Magnetostatic Energy 20

21 Lenz s Law / Induced Voltage induced electro-motive force (EMF), v emf (in volts) -- potential difference generated in a loop by applying a time-varying magnetic field B to the loop ( transformer EMF ) and/or changing the area seen by the B field over time ( motional EMF ) Iind (v induced) v emf I ind Lenz s Law ( B ind and I ind, for V emf ) -- the current induced in the loop generates a magnetic field to oppose the change in magnetic flux (B applied) 21

22 Example: Lenz s Law / Induced Voltage 22

vector directions are related by the righthand-rule, and whose magnitudes

23 Free-Space EM Waves Far away from a radiating antenna, the traveling fields may be approximated as a plane wave, with E and H in phase, whose vector directions are related by the righthand-rule, and whose magnitudes are related by the characteristic impedance of free space, h : E H h 377 W S E H 23

24 Example: Free-Space EM Waves (A) 2.6 ma/cm, parallel to the antenna (B) 3.8 ma/cm, parallel to the antenna (C) 2.6 ma/cm, perpendicular to the antenna (D) 3.8 ma/cm, perpendicular to the antenna S E H E is parallel to the antenna H is perpendicular to the antenna E H 3 10 V cm 377 W H 2.6 μa cm 377 W The correct answer is (C). 24

25 Dr. Gregory J. Mazzaro Spring 2018 Fundamentals of Engineering Exam Review Selected Advanced Circuit-Theory Concepts THE CITADEL, THE MILITARY COLLEGE OF SOUTH CAROLINA 171 Moultrie Street, Charleston, SC 29409

26 Example: RC Circuit C v t V e 0 t/ RC v 10RC V e C almost completely discharged all energy stored in C = 10 mf was dissipated by R = 25 W W CV J The correct answer is (B).

Example: RL Circuit V Rt / L il t 1e R 10 V 2.5 2.

27 Example: RL Circuit V Rt / L il t 1e R 10 V t 2 1 t il t e e A 5 W The correct answer is (D). 27

28 Example: Thevenin Equivalent 28

29 RMS or Effective Value Root-mean-squared (or effective) values are an alternative representation of the magnitude of time-varying and periodic signals. They allow us to calculate equivalent V/I/P for AC circuits as if the V/I/P quantities were DC values. 29

30 Example: Power, AC Circuit P I V I R 4W 2 rms rms rms I 4 W A W rms The correct answer is (B). 30

31 Example: Op Amp v a v a v i2 i1 0 b v b v v v v R R o a 1 a v v o v v o b 0 v R R a v The correct answer is (C). 31

32 Example: Op Amp v a v a v i2 i1 0 b v b R 4 vb v2 v2 v2 R3 R v v 0 v R R vo 1va 1 v2 R o a a R v v o The correct answer is (C). 32

33 Gain / Decibels Gain (A) refers to the ratio of output-to-input voltage, current, or power. A v V V out in differential gain = A A v,diff p V P in,1 out P in Vout V in,2 V in A v,1 A v,2 V out V A A A out v v,1 v,2 Vin A A A db db db v v,1 v,2 Decibels are a convenient mathematical form used to express very high/low gain (up/down to very high/low values of V, I, P). 33

34 Example: Op Amp, Decibels A A 20log db v,diff 10 V in,1 V 40 V V db v,diff 10 Vout V in,2 20log db The correct answer is (A). 34 A A A A db db db db p p,1 p,2 p, db

35 Transfer Function Many calculations on linear circuits, assuming the circuit has reached sinusoidal steady-state, are easier to perform in the frequency (j) domain: Y j H j X j y t h t x t by the Fourier Transform, where h is the impulse response of the circuit and H is the transfer function of the circuit 10sin t 30 V L S v v H j j kω j kω 1 kω 35 input (x) = voltage, output (y) = voltage, system (h) = voltage divider

36 Example: Transfer Function 36

37 Example: Transfer Function v 1 Vo v1 Vin v1 0 v1 v MΩ 1 jc 5 MΩ v 2 V o in 20 MΩ 1 5MΩ jc j j V V o 20j 2.7 j jc V in The correct answer is (B). 37

38 Dr. Gregory J. Mazzaro Spring 2018 Grimsley Hall, Room THE CITADEL, THE MILITARY COLLEGE OF SOUTH CAROLINA 171 Moultrie Street, Charleston, SC 29409

Physics GRE: Electromagnetism. G. J. Loges 1. University of Rochester Dept. of Physics & Astronomy. xkcd.com/567/

Physics GRE: Electromagnetism. G. J. Loges 1. University of Rochester Dept. of Physics & Astronomy. xkcd.com/567/ Physics GRE: Electromagnetism G. J. Loges University of Rochester Dept. of Physics & stronomy xkcd.com/567/ c Gregory Loges, 206 Contents Electrostatics 2 Magnetostatics 2 3 Method of Images 3 4 Lorentz