PCS130 Final Exam Master Review: Electrostatics, Circuits, Magnetism, Waves, Optics, and Nuclear Physics

Electrostatics

Core Definitions

• Electric force: The force between two electric charges, governed by Coulomb's Law.

• Electric field (E): The force per unit charge experienced by a test charge at a point in space.

• Electric potential (V): The electric potential energy per unit charge at a point.

• Potential difference (ΔV): The work done to move a charge between two points in an electric field.

Key Equations

• Coulomb's Law: $F = k \frac{q_1 q_2}{r^2}$

• Electric Field: $E = \frac{F}{q} = k \frac{q}{r^2}$

• Electric Potential: $V = k \frac{q}{r}$

• Electric Potential Energy: $U = qV$

Concepts

• Field direction: Defined as the direction of force on a positive charge.

• Charge interaction: Like charges repel; unlike charges attract.

• Superposition principle: The net electric field is the vector sum of individual fields.

Common Traps

• Forgetting to consider direction (vector nature).

• Mixing up electric field and electric force.

• Not using vector components when required.

Circuits

Definitions

• Current (I): The rate of flow of electric charge, measured in amperes (A).

• Voltage (V): The energy per unit charge, measured in volts (V).

• Resistance (R): The opposition to current flow, measured in ohms (Ω).

• Power (P): The rate at which energy is transferred or converted, measured in watts (W).

Key Equations

• Ohm's Law: $V = IR$

• Power formulas: $P = IV = I^2R = \frac{V^2}{R}$

Series vs Parallel Circuits

Comparison of properties in series and parallel circuits:

Property	Series	Parallel
Current	Same through all components	Splits among branches
Voltage	Splits across components	Same across all branches
Resistance	Adds ($R_{total} = R_1 + R_2 + ...$)	Inverse adds ($\frac{1}{R_{total}} = \frac{1}{R_1} + \frac{1}{R_2} + ...$)

Concepts

• Brightness of bulbs is proportional to power dissipated.

• Increasing resistance decreases current for a given voltage.

Common Traps

• Mixing up series and parallel rules.

• Forgetting voltage distribution rules.

Magnetism

Definitions

• Magnetic field (B): A region where a magnetic force can be detected, measured in teslas (T).

• Magnetic force: The force experienced by a moving charge in a magnetic field.

Key Equation

• Magnetic force on a moving charge: $F = qvB\sin\theta$

Right-Hand Rule

• Thumb points in direction of velocity ($v$).

• Fingers point in direction of magnetic field ($B$).

• Palm faces in direction of force for positive charge.

Concepts

• Force is zero if velocity is parallel to the field.

• Perpendicular velocity leads to circular motion.

Common Traps

• Errors in determining direction using the right-hand rule.

• Forgetting the sine factor in the equation.

Waves

Definitions

• Wavelength (\(\lambda\)): The distance between successive peaks of a wave.

• Frequency (f): The number of cycles per second, measured in hertz (Hz).

• Wave speed (v): The speed at which the wave propagates.

Core Equation

• $v = f\lambda$

Medium Changes

• Frequency remains constant when a wave changes medium.

• Speed and wavelength change depending on the properties of the new medium.

Standing Waves

• Node: Point of no motion.

• Antinode: Point of maximum motion.

• String (both ends fixed): $f_n = \frac{nv}{2L}$

• Pipes: Open pipes support all harmonics; closed pipes support only odd harmonics.

Sound

• Intensity relates to perceived loudness.

• Decibel (dB) scale is logarithmic.

Doppler Effect

• Relative motion between source and observer causes frequency shifts.

Common Traps

• Mixing up harmonics for strings and pipes.

• Confusing nodes and antinodes.

Optics

Definitions

• Refraction: Bending of light as it passes from one medium to another.

• Index of refraction (n): Ratio of speed of light in vacuum to speed in the medium.

• Critical angle: The angle of incidence for which total internal reflection occurs.

Key Equations

• Snell's Law: $n_1 \sin\theta_1 = n_2 \sin\theta_2$

• Critical Angle: $\sin\theta_c = \frac{n_2}{n_1}$

Key Concepts

• Refraction direction: Higher $n$ means slower speed and bending toward the normal; lower $n$ means faster speed and bending away from the normal.

• When light changes medium:

  • Speed changes

  • Wavelength changes

  • Frequency remains constant

Quantity	Changes?
Speed	✓
Wavelength	✓
Frequency	✗

Double Slit Interference

• Position of bright fringes: $y = \frac{m\lambda L}{d}$

• Bright fringes occur at $m\lambda$; dark fringes at $(m+\frac{1}{2})\lambda$.

Single Slit Diffraction

• Position of first minimum: $y_1 = \frac{\lambda L}{a}$

• Width of central maximum: $\text{width} = 2y_1$

Concepts

• Single slit produces a wide central maximum.

• Double slit produces evenly spaced fringes.

Common Traps

• Forgetting factor of 2 in single slit width.

• Mixing up formulas for single and double slit.

• Unit conversion errors.

Nuclear Physics

Definitions

• Mass defect: The difference between the sum of the masses of protons and neutrons and the actual mass of the nucleus; this mass is converted to binding energy.

• Binding energy: The energy required to disassemble a nucleus into its constituent protons and neutrons.

• Half-life: The time required for half of a radioactive sample to decay.

Key Equations

• Mass defect: $\Delta m = (\text{protons} + \text{neutrons}) - \text{actual mass}$

• Binding energy: $E = \Delta m \times 931 \ (\text{MeV})$

• Radioactive decay: $N = N_0 e^{-kt}$

Concepts

• Higher binding energy per nucleon indicates greater nuclear stability.

• Fusion combines nuclei; fission splits nuclei. Both processes release energy.

Common Traps

• Forgetting to include neutrons in mass calculations.

• Not converting units properly (especially mass to energy).

• Missing the 931 MeV conversion factor.

Final Exam Strategy

How to Approach Any Question

1. Identify the topic.

2. Select the appropriate formula.

3. Check units for consistency.

4. Think conceptually about the problem.

Priority Topics

• Must Master: Waves, Optics, Interference

• Important: Magnetism, Electrostatics

• Easy Marks: Nuclear Physics

Final Takeaways

• You do not need to memorize every detail.

• Focus on pattern recognition, formula recall, and avoiding common traps.