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Physics 2 Formula Sheet

This comprehensive Physics 2 formula sheet covers the essential formulas for electricity, magnetism, thermodynamics, optics, and modern physics. Keep this reference handy when solving problems or preparing for exams.

Electricity

Coulomb's Law

$$F = k_e \frac{q_1 q_2}{r^2}$$

Describes the electrostatic force between two point charges.

Symbol Meaning SI Unit
F Force between charges Newtons (N)
ke Coulomb's constant (8.99 109 Nm/C) Nm/C
q1, q2 Magnitudes of the charges Coulombs (C)
r Distance between the charges Meters (m)

Electric Field

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

Describes the electric field at a point due to a point charge.

Electric Potential

$$V = \frac{k_e Q}{r} = \frac{PE}{q}$$

Represents the electric potential at a point due to a point charge.

Capacitance

$$C = \frac{Q}{V}$$ $$C = \varepsilon_0 \frac{A}{d} \quad \text{(for parallel-plate capacitor)}$$

Ohm's Law

$$V = IR$$

The relationship between voltage, current, and resistance.

Electric Power

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

The rate at which electrical energy is transferred.

Magnetism

Magnetic Force on a Moving Charge

$$\vec{F} = q\vec{v} \times \vec{B}$$

The force exerted on a charge moving through a magnetic field.

Biot-Savart Law

$$d\vec{B} = \frac{\mu_0 I}{4\pi} \cdot \frac{d\vec{l} \times \hat{r}}{r^2}$$

Used to calculate the magnetic field produced by a current-carrying wire.

Ampre's Law

$$\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enclosed}$$

Relates the magnetic field around a closed loop to the current passing through the loop.

Magnetic Flux

$$\Phi_B = \vec{B} \cdot \vec{A} = BA\cos(\theta)$$

The measure of the number of magnetic field lines passing through a given area.

Faraday's Law of Induction

$$\varepsilon = -N\frac{\Delta\Phi_B}{\Delta t}$$

The induced electromotive force in a closed loop equals the negative rate of change of magnetic flux through the loop.

Inductance

$$N\Phi_B = LI$$ $$\varepsilon = -L\frac{\Delta I}{\Delta t}$$

Defines inductance and the induced emf when current changes.

Thermodynamics

First Law of Thermodynamics

$$\Delta U = Q - W$$

The change in internal energy of a system equals the heat added to the system minus the work done by the system.

Ideal Gas Law

$$PV = nRT$$

Relates pressure, volume, temperature, and number of moles of an ideal gas.

Heat Transfer

$$Q = mc\Delta T \quad \text{(thermal energy)}$$ $$Q = mL \quad \text{(phase change)}$$

Heat transfer causing temperature change or phase change.

Second Law of Thermodynamics

$$\Delta S \ge \frac{Q}{T}$$

The entropy of an isolated system always increases in natural processes.

Carnot Engine Efficiency

$$e = 1 - \frac{T_c}{T_h} = \frac{T_h - T_c}{T_h}$$

The maximum theoretical efficiency of a heat engine operating between two temperatures.

Optics

Snell's Law

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

Relates the angles of incidence and refraction to the refractive indices of the two media.

Index of Refraction

$$n = \frac{c}{v}$$

The ratio of the speed of light in vacuum to its speed in a medium.

Mirror and Lens Equation

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

Relates the focal length, object distance, and image distance.

Magnification

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

The ratio of image height to object height.

Young's Double-Slit Experiment

$$d\sin(\theta) = m\lambda \quad \text{(for bright fringes)}$$

Describes the interference pattern from two coherent light sources.

Modern Physics

Photoelectric Effect

$$E_k = hf - \Phi$$

The maximum kinetic energy of emitted electrons is proportional to the frequency of incident light.

Photon Energy

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

The energy of a photon is related to its frequency and wavelength.

de Broglie Wavelength

$$\lambda = \frac{h}{p} = \frac{h}{mv}$$

All matter exhibits wave-like properties with a wavelength inversely proportional to its momentum.

Mass-Energy Equivalence

$$E = mc^2$$

The equivalence of mass and energy.

Bohr Model

$$E_n = -\frac{13.6 \text{ eV}}{n^2}$$ $$r_n = n^2 a_0$$

Energy levels and orbital radii in the hydrogen atom.

Radioactive Decay

$$N = N_0 e^{-\lambda t}$$ $$\lambda = \frac{\ln(2)}{t_{1/2}}$$

The exponential decay of radioactive nuclei.

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