PHYS 202 OUTLINE FOR PART I

ELECTRICITY

Dr. Johnny B. Holmes

Electric Forces and Electric Fields

1. Electric force (vector)   S-1,2,3
1. four fundamental forces: gravity, E&M, two nuclear
2. Coulomb's Law: F = k q1 q2 / r²            (similar to F = G m1 m2 / r²)
3. protons and electrons: charge (q) and mass (m)
1. proton: q = +e = +1.6 x 10-19 C; m = 1.67 x 10-27 kg
2. electron: q = -e = -1.6 x 10-19 C; m = 9.11 x 10-31 kg
4. insulators and conductors
2. Electric field      S-4
1. definition: E º F(on qt) / qt (a vector)
2. units: Nt/Coul (or Volt/meter; see below)
3. for point charge, magnitude: E = k q / r² , direction: points away from +q, toward -q
4. for several charges: add as vectors (express in POLAR, but add in RECTANGULAR)

1. At a particular instant a particle of mass mA = 5 mg and charge of qA = 5 m Coul is located at the origin. A second particle of mass mb = 2 mg and charge of qB = -6 m Coul is located at that same instant at a position (-5 m, +3 m) relative to the origin. a) What is the force on qA due to the presence of qB ? b) Is the magnitude of the force on qB due to the presence of qA the same, greater or smaller than the magnitude of the force on qA due to the presence of qB ? c) Assuming the two charges have no other forces on them, what is the magnitude of the resulting acceleration of particle A due to the electrical interaction with particle A? d) Is the acceleration of particle B due to the presence of particle A the same, greater or smaller than the magnitude of the acceleration of particle A?

2. In the hydrogen atom the electron orbits the proton at a distance of 5 x 10-11 meters. a) What is the electric force on the electron due to the proton? b) What is the velocity of the electron in its orbit about the proton? [HINT: use S F=ma and recall for circular motion that a=v²/r.]

3. a) What is the magnitude of the gravitational force between the proton and the electron when they are separated by 1 nm? b) What is the electrical force between the proton and the electron when they are separated by 1 nm? c) Which force is the stronger? d) How many significant figures would have to be used before the weaker force would alter the net force from being equal to the stronger force? [EXAMPLE: if F1=1.000 Nt and F2=0.01 Nt, then Fnet=F1 to 2 significant figures (1.0), but the third significant figure would be changed (1.01 instead of 1.00).]

4. Consider two charges: qA has a charge of 5 nCoul and is located at (5 m, 3 m); qB has a charge of -4 nCoul and is located at (7 m, -2 m). a) What is the electric field at the origin due to qA alone? b) What is the electric field at the origin due to BOTH charges?

1. (a) 7.94x10-3 Nt; (b) same; (c) 1,588 m/s²; (d) acceleration of B is larger.

2. a) 9.2 x 10-8 Nt; b) 2.2 x 106 m/s.

3. a) 1.01 x 10-49 Nt; b) 2.3 x 10-10 Nt; c) electrical; d) 39.

4. a) E = 1.32 Nt/Coul at 211°; (b) E = .99 Nt/Coul at 241°

Electrical Energy and Capacitance

1. Electric potential (Voltage, EMF)          S-5,6,7
1. definition: V º PE(of qt) / qt        (a scalar)
2. units: Volt = Joule / Coul
3. for point charge, V = k q /r (+ for +q, - for -q)
4. for several charges, add as scalars
5. use in conservation of energy: PEel = q V
6. related to field: Ex = -DV / Dx; Ey = -DV / Dy
2. Electron beams             S-8
1. conservation of energy
2. x-ray tubes
3. Cathode Ray Tubes (CRT): T.V.'s, monitors, oscilloscopes
3. Capacitance     S-9
1. definition: C º Q / V     [stores charge and hence energy]
2. units: Farad = Coul / Volt
3. geometry: for parallel plate, C = K A / 4 p k d

[K is dielectric constant, A is area, d is distance, k is Coulomb's constant]

1. energy stored: Energy = 1/2 Q V = 1/2 C

Supplementary Problems (S-):

5. Consider two charges (same as for problem S-4): qA has a charge of 5 nCoul and is located at (5 m, 3 m); qB has a charge of -4 nCoul and is located at (7 m, -2 m). a) What is the electric potential at the origin due to qA alone? b) What is the electric potential at the origin due to BOTH charges?

6. What change in potential energy does a +6 microCoulomb charge experience in moving from a position where the potential is 60 volts to one where it is 35 volts? Express your answer in Joules and in eV. If the charge has a mass of 2 mg, and the charge was initially at rest, and if all the potential energy change went into changing the particles kinetic energy, how fast would the particle be going when it reached the 35 volt position?

7. a) Through how many volts will an electron have to be accelerated if it is to reach 1 million miles/hr if it starts from rest? b) Will the electron need to fall through twice the voltage difference to go twice as fast? c) Through how many volts will a proton have to be accelerated if it is to reach 1 million miles/hr if it starts from rest?

8. Be able to describe how a CRT works.

9. a) If a 2 m F capacitor is charged up with a 12 volt battery, how much energy is stored in the capacitor? b) How much charge is stored on the capacitor? Now suppose that half the charge is drained off the capacitor. c) Will the voltage also be decreased by a factor of 2 (that is, 1/2) - if not, by what factor is it changed? d) Will the energy stored also be decreased by a factor of 2 - if not, by what factor is it changed?

5. a) +7.72 volts; b) +2.77 volts.

6. decrease of 1.5x10-4 Joules = 9.37x1014 eV; 12.25 m/sec = 27.4 mph.

7. a) 0.57 volts; b) no, four times the voltage difference; c) 1,040 volts.

9. a) 144 mJ or .144 m J; b) 24 m C; c) Yes; d) No, decreased by a factor of 2² or 4 (that is, by 1/4).

Current and Resistance

1. Current
1. definition: I º Dq / Dt
2. units: Ampere = Coul / sec
2. Voltage, current, and resistance             S-10,11
1. Ohm's Law: V = I R
2. RESISTANCE: R = r L / A where r is resistivity
3. POWER: P = I V = I² R = V² / R (Watt = Volt Amp)

10. A 60 Watt light bulb is designed to work with a 110 volt power supply. a) What is the current through the light bulb? b) What is the resistance of the light bulb? c) Does a 100 Watt light bulb have a lower or higher resistance than the 60 Watt bulb?

11. From the Capacitance and Dielectrics part D, energy stored in a capacitor is PE = 1/2QV. From the Current & Resistance part C, PE = QV. Explain why there is a 1/2 in the one but not the other equation.

10. a) 0.55 Amps; b) 200 W; c) less.

Direct Current Circuits

1. Resistive circuits           S-12
1. series: Rtotal = R1 + R2 + ... = S Ri            (more length - harder - bigger R)
2. parallel: (1/Rtotal) = (1/R1) + (1/R2) +... = S (1/Ri)          (more area - easier - less R)