🎯⭐ INTERACTIVE LESSON

Physics: Electricity & Optics

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Physics: Electricity & Optics - Complete Interactive Lesson

Part 1: Electrostatics & Coulombs Law

Physics: Electricity, Magnetism & Optics

Part 1 of 7 — Electrostatics

Coulomb's Law

$F = k\frac{q_1 q_2}{r^2} \qquad k = 8.99 \times 10^9\;\text{N}\cdot\text{m}^2/\text{C}^2$

Like charges repel, opposite charges attract
Force is proportional to $1/r^2$ (inverse square law)

Electric Field

$\vec{E} = \frac{F}{q} = k\frac{Q}{r^2}$

Points AWAY from positive charges, TOWARD negative charges
Units: N/C or V/m

Electric Potential (Voltage)

$V = k\frac{Q}{r} \qquad \Delta V = -\int \vec{E}\cdot d\vec{r}$

Electric Potential Energy

$U = k\frac{q_1 q_2}{r} = qV$

Positive charges move from high V to low V spontaneously
Negative charges move from low V to high V spontaneously

Equipotential Insight

Moving along an equipotential surface requires no work by the electric field because $\Delta V = 0$ .

Electrostatics 🎯

Key Takeaways — Part 1

Coulomb's law: $F \propto q_1 q_2/r^2$ , same form as gravity
E-field points away from +, toward −
(scalar, not vector — easier to calculate!)

Part 2: Electric Circuits

Physics: Electricity, Magnetism & Optics

Part 2 of 7 — Circuits (HIGH YIELD)

Ohm's Law

$V = IR$

Kirchhoff's Laws

Junction Rule: Current in = current out ( $\sum I_{in} = \sum I_{out}$ )

Part 3: Magnetism & EM Induction

Physics: Electricity, Magnetism & Optics

Part 3 of 7 — Magnetism

Magnetic Force on a Moving Charge

$F = qvB\sin\theta$

Direction: Right-hand rule (fingers from $\vec{v}$ to , thumb = )

Part 4: Optics & Light

Physics: Electricity, Magnetism & Optics

Part 4 of 7 — Optics: Reflection & Refraction

Law of Reflection

$\theta_{incident} = \theta_{reflected}$

Part 5: Nuclear Physics & Radioactivity

Physics: Electricity, Magnetism & Optics

Part 5 of 7 — Lenses & Mirrors

Thin Lens / Mirror Equation

$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$

Part 6: Electrochemistry

Physics: Electricity, Magnetism & Optics

Part 6 of 7 — Electromagnetic Spectrum & Light

The EM Spectrum (increasing frequency/decreasing wavelength)

Radio → Microwave → Infrared → Visible → Ultraviolet → X-ray → Gamma

$c = f\lambda = 3 \times 10^8\;\text{m/s}$

Visible Light

Red (700 nm) → Orange → Yellow → Green → Blue → Violet (400 nm)

Part 7: Review & MCAT Practice

Physics: Electricity, Magnetism & Optics

Part 7 of 7 — Atomic & Nuclear Physics

Atomic Models on the MCAT

Bohr model: Electrons in quantized orbits. $E_n = -13.6/n^2$ eV (for hydrogen).
Photon emitted when electron drops levels: $E = h f = E_{h}$

Potential energy:

U = kq_1q_2/r = qV

Loop Rule: Total voltage around a loop = 0 (

\sum V = 0

)

Series vs. Parallel Resistors

Configuration	Resistance	Current	Voltage
Series	$R_T = R_1 + R_2 + ...$	Same through each	Divides
Parallel	$\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + ...$

$P = IV = I^2R = \frac{V^2}{R}$

$C = \frac{Q}{V} \qquad U = \frac{1}{2}CV^2$

Series: $\frac{1}{C_T} = \frac{1}{C_1} + \frac{1}{C_2}$ (OPPOSITE of resistors!)
Parallel: $C_T = C_1 + C_2$

Capacitors resist instantaneous voltage change, which is why they smooth signals and create charging/discharging time constants in physiology instrumentation contexts.

Key Takeaways — Part 2

Series: same current, voltages add, $R_{total}$ increases
Parallel: same voltage, currents add, $R_{total}$ decreases
Capacitors add OPPOSITE to resistors! (parallel: $C$ adds; series: $1/C$ adds)
$P = IV = I^2R = V^2/R$ — know all three forms

Force is PERPENDICULAR to both velocity and field

Stationary charges feel NO magnetic force

Circular Motion in a Magnetic Field

$qvB = \frac{mv^2}{r} \implies r = \frac{mv}{qB}$

Force on a Current-Carrying Wire

Electromagnetic Induction (Faraday's Law)

$\varepsilon = -\frac{d\Phi_B}{dt}$

Changing magnetic flux induces an EMF (voltage)
Lenz's Law: Induced current opposes the change that caused it

Flux changes can come from changing field strength, loop area, or orientation relative to the field.

Key Takeaways — Part 3

Magnetic force: $F = qvB\sin\theta$ (zero when parallel!)
Magnetic force does NO work (always perpendicular to velocity)
Right-hand rule for direction: point fingers from $\vec{v}$ to $\vec{B}$
Faraday: changing flux → induced EMF; Lenz: opposes the change

(Angles measured from the normal!)

Snell's Law (Refraction)

$n_1\sin\theta_1 = n_2\sin\theta_2$

$n$ = index of refraction ( $n = c/v$ , always $\ge 1$ )
Light bends TOWARD normal when entering denser medium ( $n_2 > n_1$ )
Light bends AWAY from normal when entering less dense medium

Total Internal Reflection

$\sin\theta_c = \frac{n_2}{n_1} \quad (n_1 > n_2)$

Only occurs when going from denser to less dense medium
Angle of incidence must exceed the critical angle
Applications: fiber optics, diamond sparkle

Higher refractive index means lower light speed in that medium ( $n=c/v$ ).

Optics: Refraction 🎯

Key Takeaways — Part 4

Snell's law: $n_1\sin\theta_1 = n_2\sin\theta_2$
Entering denser medium → bend toward normal (slower speed)
Total internal reflection: only denser → less dense, beyond critical angle
All angles measured from the NORMAL, not the surface!

$m = -\frac{d_i}{d_o} = \frac{h_i}{h_o}$

$|m| > 1$ : enlarged; $|m| < 1$ : reduced
$m > 0$ : upright; $m < 0$ : inverted

Quantity	Positive	Negative
$d_o$	Object on same side as incoming light	(Virtual object)
$d_i$	Image on opposite side (real)	Same side as object (virtual)
$f$	Converging (convex lens/concave mirror)	Diverging (concave lens/convex mirror)

Concave mirror / Convex lens: Converging, $f > 0$
Convex mirror / Concave lens: Diverging, $f < 0$ , always produces virtual, upright, reduced image

Always interpret sign of $d_i$ and $m$ before choosing the image description.

Lenses & Mirrors 🎯

Key Takeaways — Part 5

$1/f = 1/d_o + 1/d_i$ — works for both lenses and mirrors
Diverging elements ( $f < 0$ ): always virtual, upright, reduced
Sign of $d_i$ tells you real (+) vs virtual (−)
Sign of $m$ tells you inverted (−) vs upright (+)

E = hf = \frac{hc}{\lambda}

E = h f = \frac{h c}{λ}

Higher frequency = higher energy = shorter wavelength

Photoelectric Effect

$KE_{max} = hf - \phi$

$\phi$ = work function (minimum energy to eject electron)
Below threshold frequency: NO electrons ejected, regardless of intensity
Above threshold: intensity affects NUMBER of electrons, not their energy

Diffraction & Interference

Constructive: $d\sin\theta = n\lambda$ (bright fringes)
Destructive: $d\sin\theta = (n + \frac{1}{2})\lambda$ (dark fringes)

Below threshold frequency, no electrons are emitted regardless of light intensity because single photons do not carry enough energy.

Light & Quantum 🎯

Key Takeaways — Part 6

$E = hf = hc/\lambda$ : higher frequency = higher energy
Photoelectric effect: threshold frequency matters, not intensity
EM spectrum order: Radio < Micro < IR < Visible < UV < X-ray < Gamma
Double-slit: demonstrates wave nature of light (interference pattern)

E = h f = E_{hi g h} - E_{l o w}

$^A_Z X \qquad A = \text{mass number}, Z = \text{atomic number}$

Radioactive Decay Types

Type	Particle	Change in $A$	Change in $Z$
Alpha ( $\alpha$ )	$^4_2\text{He}$	$-4$	$-2$
Beta $^-$ ( $\beta^-$ )	Electron	$0$	$+1$
Beta $^+$ ( $\beta^+$ )	Positron	$0$	$-1$
Gamma ( $\gamma$ )	Photon	$0$	$0$

$N = N_0\left(\frac{1}{2}\right)^{t/t_{1/2}}$

After $n$ half-lives: $N = N_0/2^n$

Activity is proportional to number of undecayed nuclei, so activity falls exponentially with the same half-life behavior.

Nuclear Physics 🎯

Physics E&M/Optics — Complete! ✅

Master circuits, optics (lens/mirror equation), and nuclear decay. These are the most tested physics topics. Remember: the MCAT is more conceptual than computational — understand WHY, not just how to calculate.

Physics: Electricity & Optics

Series vs. Parallel Resistors

Power

Capacitors

RC Intuition

Key Takeaways — Part 2

Circular Motion in a Magnetic Field

Force on a Current-Carrying Wire

Electromagnetic Induction (Faraday's Law)

Key Takeaways — Part 3

Snell's Law (Refraction)

Total Internal Reflection

Key Takeaways — Part 4

Magnification

Sign Conventions

MCAT Must-Know

Key Takeaways — Part 5

Photoelectric Effect

Diffraction & Interference

Key Takeaways — Part 6

Nuclear Physics

Radioactive Decay Types

Half-Life

Physics E&M/Optics — Complete! ✅