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 test charge.

• Charge interactions: 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).

• Confusing electric field with electric force.

• Neglecting vector components in calculations.

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

• Confusing series and parallel circuit rules.

• Forgetting voltage distribution in circuits.

Magnetism

Definitions

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

• Magnetic force: The force exerted on 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 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 force equation.

Waves

Definitions

• Wavelength (λ): The distance between successive peaks or troughs.

• 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 according to the properties of the new medium.

Standing Waves

• Node: Point of zero 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 open and closed 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: Angle of incidence for total internal reflection.

Key Equations

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

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

Refraction Direction

• Higher index ($n$) means slower speed; light bends toward the normal.

• Lower index means faster speed; light bends away from the normal.

What Changes When Light Enters a New Medium?

Quantity	Changes?
Speed	Yes
Wavelength	Yes
Frequency	No

Double Slit Interference

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

• Bright fringe condition: $m\lambda$

• Dark fringe condition: $(m+\frac{1}{2})\lambda$

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 separate 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: $N = N_0 e^{-kt}$