Electrostatics/Electromagnetism

Practice Exam 1 Solutions Notes

Problem 1:
- Electric force vectors: Sum and components
- Given forces: $Fn$ and $Fl$
- Volumes for calculation: 15µL and 13µL
- Force equations:
  - Horizontal component calculation:
  - $Fx = K{9,93} imes ext{cos}(37^{ ext{o}}) = 76.0 ext{N}$
  - Vertical component calculation:
  - $Fy = K{qz qz} imes ext{sin}(37^{ ext{o}}) = 1370 ext{N}$
- Total Electrostatic Force:
  - Magnitudes: $F_{ ext{total}} = 76.0 ext{N}$ and $1370 ext{N}$
Problem 2:
- Electric field definition:
- The electric field, $E$, at a point in space measures force per unit charge, expressed as:
  - E = rac{F}{q}
Problem 3:
- Force on charge in an electric field:
- Equation:
  - F_E = qE
- Components:
  - $F_x = T ext{sin}( heta)$
  - $F_y = T ext{cos}( heta) = mg$
- Setting equations equal:
  - T ext{cos}(0) = mg
  - Resulting equations:
  - E = rac{mg}{T ext{tan}( heta)}
  - Example calculation yields:
  - E = 2.40 imes 10^{3} ext{N/C}
Problem 4:
- Electric field dependence:
- Statement: Magnitude of the electric field does depend on the sign of the charge causing the field.
- Important equation:
  - E = k rac{q}{r^2}

Problem 5:
- Electric fields canceling out:
- Given charge situation:
  - Total Electric Field, $E_{ ext{net}}$, from charges (considering directions)
  - Calculation yields:
  - E = 1.80 imes 10^4 ext{N/C}
Problem 6:
- Voltage and capacitance relationship under power:
- Given the capacitor behavior when connected to power:
  - $Va = K rac{E0 A}{d}$
  - Final charge equation:
  - Q_{ ext{new}} = 2Q
Problem 7:
- Resistors in parallel:
- Total resistance decrease leads to increased total current:
- Ohm's Law:
  - V = I R

Problem 8:
- Equivalent resistance calculation for configurations:
- Calculate total:
  - R_{ ext{total}} = R + R = rac{8}{8} + 16
  - Yield current:
  - Total current of $1.50 ext{A}$
Problem 9:
- Voltage across resistors:
- For $8 ext{ } ext{Ω}$ resister:
  - V_g = I R = 1.50 ext{A} imes 8 ext{Ω} = 12.0 ext{V}
- Two parallel resistor voltage:
  - V{ice} = Vg = 12.0 ext{V}
Problem 10:
- Current through resistors using Kirchhoff’s laws:
- $I_{in}$ distributions:
  - Left Loop: Analyze points yielding currents $I_z$, etc.
  - Resulting currents identified through unary equations:
  - I = 0.67 + 0.15

Problem 11:
- Misconception about magnetic forces:
- False statement: Magnetic force increases speed.
- Clarification: Magnetic force does NOT increase the speed due to the perpendicular nature to velocity.
Problem 12:
- Work-energy theorem application:
- W_{ ext{net}} = KE = q imes DV
- Formulate final energy values:
  - Combine forces:
  - F = qvB ext{sin}( heta)
Problem 13:
- Magnetic field relationships:
- Rule detailing how forces can oppose each other:
  - Resulting calculations on magnetic interaction
  - Derived constants noted.

Problem 14:
- Changes in magnetic flux induce currents:
- Relationship established through defined equations.
Problem 15:
- Power input and output relationship:
- Recognizing values through series definitions:
  - P{input} = Ip V_p = 150A imes 6000V = 9.0 imes 10^{5}W
  - Establish total power calculations based on resistances:
  - Including efficiency evaluations for outputs at calculated amperage.
END OF PRACTICE EXAM SOLUTIONS