Overview
Work on the Study Guide for Physics 236 Finals
Study Guide Final Exam - Physics 236
- Electric Potential
Summary:
Electric potential is the amount of electric potential energy per unit charge at a point in space. It is a scalar quantity and is measured in volts (V). The electric potential due to a point charge decreases with distance. Electric potential is path-independent and is useful for calculating energy changes in electrostatic systems.
General Equations:
V = kQ/r W = qΔVTrue/False Questions:
1. Electric potential is a scalar quantity. True or False(True)
2. Potential difference is the same as electric field strength. True or False(False)
Multiple Choice Questions:
1. The unit of electric potential is: A) Joule B) Tesla C) Coulomb D) VoltD) Volt
2. Which quantity affects electric potential the most? A) Electric field strength, B) Distance and charge magnitude, C) Charge density, D) Permittivity of free spaceB) Distance and charge magnitude
Numerical Problems: (Show Full Explanations)
1. Find the potential 0.4 m from a 6 μC charge. → 135,000 V - Correct Answer/same answer 2. How much work is done moving 3 μC across 50 V? → 1.5 × 10⁻⁴ J - Correct Answer/same answer- Electric Fields
Summary:
Electric fields describe the force experienced by a unit charge placed in space. The field is a vector pointing away from positive charges and toward negative charges. It is stronger near the source and weaker with distance. Electric fields are central to understanding how charges interact.
General Equations:
E = F/q E = kQ/r²True/False Questions:
1. Electric fields point from positive to negative charges. True or False(True)
2. Electric field inside a conductor is nonzero. True or False(False)
Multiple Choice Questions:
1. SI unit of electric field is: A) V/m, B) N/C, C) V/m², D) A/mB) N/C
2. The field from a point charge decreases with: A) r², B) r, C) 1/r², D) 1/rA) r²
Numerical Problems: (Show Full Explanations)
1. Compute E 0.2 m from a 5 μC charge. → 1.125 × 10⁶ N/C - Correct Answer/same answer 2. Force on 4 μC in a 600 N/C field? → 0.0024 N - Correct Answer/same answer- Gauss’s Law
Summary:
Gauss’s Law relates the electric flux through a closed surface to the net charge enclosed by that surface. It is especially useful in cases of high symmetry (spheres, cylinders, planes). The electric field can be calculated more easily than with Coulomb’s law when symmetry is present.
General Equations:
Φ_E = ∮ E·dA = Q_enc/ε₀True/False Questions:
1. Gauss’s Law applies to symmetric charge distributions. True or False(True)
2. Electric flux depends on surface shape, not charge. True or False(False)
Multiple Choice Questions:
1. Which is true of electric flux? A) It is scalar, B) It is vector, C) It depends only on the electric strength, D) It is always positiveA) It is scalar
2. Best Gaussian surface for a point charge is: A) Cube, B) Cylinder, C) Sphere, D) PlaneC) Sphere
Numerical Problems: (Show Full Explanations)
1. Calculate flux for 2 μC charge. → 2.26 × 10⁵ Nm²/C - Correct Answer/same answer 2. Find Q_enc if Φ = 4 × 10⁵ Nm²/C. → 3.54 × 10⁻⁶ C - Correct Answer/same answer- Faraday’s Law
Summary:
Faraday’s Law of electromagnetic induction states that a changing magnetic field within a closed loop induces an electromotive force (EMF). This EMF drives a current if the circuit is complete. The direction of the induced current opposes the change in magnetic flux, as described by Lenz’s Law.
General Equations:
ε = -dΦB/dt ΦB = B·A·cos(θ)True/False Questions:
1. A changing magnetic field can induce an electric current. True or False(True)
2. Faraday’s Law works only with steady magnetic fields. True or False(False)
Multiple Choice Questions:
1. Faraday’s Law relates induced EMF to: A) Circuit resistance, B) Magnetic flux change, C) Strength of magnetic field only, D) Speed of conductor moving through the magnetic fieldB) Magnetic flux change
2. Lenz’s Law determines: A) Magnitude of induced current, B) Resistance in the circuit, C) Direction of induced current, D) Speed of the magnetic fieldC) Direction of induced current
Numerical Problems: (Show Full Explanations)
1. A coil's flux changes from 0.4 Wb to 0.1 Wb in 0.2 s. Find EMF. → 1.5 V - Correct Answer/same answer 2. A 0.05 m² loop in a 0.3 T field rotates 90° in 0.5 s. → 0.03 V - Correct Answer/same answer- DC and AC Circuits
Summary:
DC (direct current) circuits involve constant current and voltage in one direction, while AC (alternating current) circuits involve sinusoidally varying currents. RMS (root mean square) values represent effective current and voltage in AC systems. AC circuits are used for power distribution, while DC is common in batteries and electronics.
General Equations:
V = IR P = IV V(t) = V₀sin(ωt) V_rms = V₀/√2 I_rms = I₀/√2True/False Questions:
1. In DC, current flows in one direction. True or False(True)
2. RMS current is greater than peak current. True or False(False)
Multiple Choice Questions:
1. Household AC frequency in US: A) 50 Hz, B) 60 Hz, C) 100 Hz, D) 220 HzB) 60 Hz
2. AC voltage varies as: A) Sinusoidal function, B) Square wave, C) Triangular wave, D) Sawtooth waveA) Sinusoidal function
Numerical Problems: (Show Full Explanations)
1. 100 W bulb on 120 V → I = 0.833 A - Correct Answer/same answer 2. If V₀ = 170 V → V_rms = 120 V - Correct Answer/same answer- RLC Circuits
Summary:
RLC circuits combine resistance (R), inductance (L), and capacitance (C). In AC, they produce impedance (Z), a frequency-dependent combination of resistance and reactance. At resonance, inductive and capacitive reactance cancel, and the circuit's impedance is minimized.
General Equations:
X_L = ωL X_C = 1/ωC Z = √(R² + (X_L - X_C)²) f₀ = 1/(2π√(LC))True/False Questions:
1. At resonance, impedance is minimum. True or False(True)
2. Inductive reactance decreases with frequency. True or False(False)
Multiple Choice Questions:
1. Resonant frequency is: A) 1/2π(L), B)1/2π(C), C) 1/(2π√(LC)), D) L * CB) 1/(2π√(LC))
2. Impedance is: A) The total opposition to current in an AC circuit, B) A measure of voltage in a circuit, C) Combination of resistance and reactance, D) A type of resistance that does not change with frequencyC) Combination of resistance and reactance
Numerical Problems: (Show Full Explanations)
1. L = 0.2 H, C = 80 μF → f₀ ≈ 125.3 Hz - Correct Answer/same answer 2. R = 10 Ω, X_L = 40 Ω, X_C = 20 Ω → Z ≈ 22.4 Ω - Correct Answer/same answer- Magnetic Fields
Summary:
Magnetic fields arise from moving electric charges. They exert forces on other moving charges and form closed loops. The field around a current-carrying wire depends on current and distance. The force on a charge depends on its velocity, the field, and the angle between them.
General Equations:
F = qvB sin(θ) B = μ₀I/(2πr) Φ_B = B·A·cos(θ)True/False Questions:
1. Magnetic field lines form closed loops. True or False(True)
2. A stationary charge in a magnetic field experiences a force. True or False(False)
Multiple Choice Questions:
1. Direction of magnetic force is found using: A) Faraday’s law, B) Ampere’s law, C) Right-hand rule, D) Left-hand ruleC) Right-hand rule
2. Magnetic field unit is: A) Weber, B) Newton, C) Ampere, D) TeslaD) Tesla
Numerical Problems: (Show Full Explanations)
1. Find B 0.05 m from 6 A wire → 2.4 × 10⁻⁵ T - Correct Answer/same answer 2. Force on 3 μC at 200 m/s in 0.4 T → 2.4 × 10⁻⁴ N - Correct Answer/same answer- Inductance
Summary:
Inductance is the property of a coil that resists changes in current. An inductor generates a back EMF proportional to the rate of change of current. Energy is stored in its magnetic field. Inductors are used in filters, transformers, and oscillators.
General Equations:
V = L(dI/dt) U = 1/2 LI²True/False Questions:
1. Inductors resist changes in current. True or False(True)
2. Induced EMF in an inductor is always zero. True or False(False)
Multiple Choice Questions:
1. Unit of inductance is: A) Henry, B) Ohm, C) Tesla, D) WeberA) Henry
2. Energy is stored in an inductor's: A) Electric field, B) Electrostatic field, C) Magnetic field, D) both electric and magnetic fieldsC) Magnetic field
Numerical Problems: (Show Full Explanations)
1. L = 0.5 H, ΔI = 3 A, Δt = 0.2 s → V = 7.5 V - Correct Answer/same answer 2. L = 2 H, I = 4 A → U = 16 J - Correct Answer/same answer- Electromagnetic Waves
Summary:
Electromagnetic (EM) waves consist of oscillating electric and magnetic fields propagating through space at the speed of light. They include radio, microwave, infrared, visible, UV, X-rays, and gamma rays. EM waves are transverse and do not require a medium.
General Equations:
c = 1/√(μ₀ε₀) E = cB v = fλTrue/False Questions:
1. EM waves can travel through a vacuum. True or False(True)
2. Electric and magnetic fields in EM waves are parallel. True or False(False)
Multiple Choice Questions:
1. EM waves are: A) Longitudinal, B) Transverse, C) Both longitudinal and transverse, D) Neither longitudinal or transverseB) Transverse
2. The ratio E/B equals: A) Speed of radio waves, B) Speed of infrared waves, C) Speed of gamma rays, D) Speed of lightD) Speed of light
Numerical Problems: (Show Full Explanations)
1. If B = 1.5 × 10⁻⁶ T → E = 450 V/m - Correct Answer/same answer 2. f = 6 × 10¹⁴ Hz → λ = 5 × 10⁻⁷ m - Correct Answer/same answerPlease show full explanations of the numerical problems in all topics.