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Showing 24 of 258 formulas Page 4 of 11

Lens Maker's Formula

Physics β†’ Optics β†’ Ray Optics β†’ Lenses
$$\frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)$$
Relates the focal length of a lens to the refractive index of its material and the radii of curvature of its surfaces.
πŸ“– Physics πŸ“š Ray Optics

Coulomb's Law in Dielectrics

Physics β†’ Electromagnetism β†’ Electrostatics β†’ Electric Force
$$F = \frac{1}{4\pi\epsilon_0\epsilon_r} \frac{q_1q_2}{r^2}$$
Calculates the electrostatic force between two charges when placed in a dielectric medium.
πŸ“– Physics πŸ“š Electrostatics

Bohr's Frequency Condition

Physics β†’ Atomic Physics β†’ Atomic Structure β†’ Photon Emission
$$\Delta E = hf = E_2 - E_1$$
Relates the frequency of light emitted or absorbed to the change in energy levels of an electron in an atom.
πŸ“– Physics πŸ“š Atomic Structure

Magnetic Force on a Moving Charge

Physics β†’ Electromagnetism β†’ Magnetic Effects of Current β†’ Lorentz Force
$$F = qvB \sin \theta$$
Calculates the force exerted by a magnetic field on a particle with charge $q$ moving with velocity $v$.
πŸ“– Physics πŸ“š Magnetic Effects of Current

Work Done by Constant Force

Physics β†’ Mechanics β†’ Work and Energy β†’ Work
$$W = Fd \cos \theta$$
The energy transferred to or from an object via the application of force along a displacement.
πŸ“– Physics πŸ“š Work and Energy

Ohm's Law (Microscopic Form)

Physics β†’ Electromagnetism β†’ Current Electricity β†’ Conductivity
$$\vec{J} = \sigma \vec{E}$$
Relates current density to the electric field within a conductor.
πŸ“– Physics πŸ“š Current Electricity

Einstein's Photoelectric Equation

Physics β†’ Quantum Mechanics β†’ Dual Nature of Matter β†’ Photoelectric Effect
$$K_{\max} = hf - \Phi$$
Relates the maximum kinetic energy of emitted photoelectrons to the frequency of incident light and the work function of the material.
πŸ“– Physics πŸ“š Dual Nature of Matter

Centripetal Force (Angular Form)

Physics β†’ Mechanics β†’ Circular Motion β†’ Dynamics
$$F_c = m\omega^2r$$
Expresses centripetal force in terms of angular velocity.
πŸ“– Physics πŸ“š Circular Motion

Young's Modulus

Physics β†’ Mechanics β†’ Elasticity β†’ Stress and Strain
$$Y = \frac{FL_0}{A\Delta L}$$
Measures the stiffness of a solid material.
πŸ“– Physics πŸ“š Elasticity

Angular Momentum of a Point Mass

Physics β†’ Mechanics β†’ Rotational Motion β†’ Angular Momentum
$$L = mvr \sin \theta$$
The rotational equivalent of linear momentum for a particle.
πŸ“– Physics πŸ“š Rotational Motion

Pressure of an Ideal Gas (Kinetic Theory)

Physics β†’ Thermodynamics β†’ Kinetic Theory β†’ Gas Pressure
$$P = \frac{1}{3} \frac{Nm\bar{v^2}}{V}$$
Relates the microscopic motion of gas molecules to the macroscopic pressure.
πŸ“– Physics πŸ“š Kinetic Theory

Efficiency of a Heat Engine

Physics β†’ Thermodynamics β†’ Second Law β†’ Heat Engines
$$\eta = 1 - \frac{Q_L}{Q_H}$$
Measures the fraction of heat energy converted into useful work.
πŸ“– Physics πŸ“š Second Law

Biot-Savart Law (Infinite Wire)

Physics β†’ Electromagnetism β†’ Magnetism β†’ Magnetic Fields of Current
$$B = \frac{\mu_0 I}{2\pi r}$$
Calculates the magnetic field at a distance $r$ from an infinitely long straight wire.
πŸ“– Physics πŸ“š Magnetism

Surface Tension Formula

Physics β†’ Fluid Mechanics β†’ Properties of Liquids β†’ Surface Tension
$$\gamma = \frac{F}{L}$$
The force per unit length exerted parallel to the surface of a liquid.
πŸ“– Physics πŸ“š Properties of Liquids

Terminal Velocity

Physics β†’ Mechanics β†’ Dynamics β†’ Drag Force
$$v_t = \sqrt{\frac{2mg}{\rho AC_d}}$$
The constant speed reached by a falling object when the drag force equals the gravitational force.
πŸ“– Physics πŸ“š Dynamics

Young's Double Slit (Fringe Width)

Physics β†’ Optics β†’ Wave Optics β†’ Interference
$$\beta = \frac{\lambda D}{d}$$
Calculates the distance between two consecutive bright or dark fringes in an interference pattern.
πŸ“– Physics πŸ“š Wave Optics

Self-Inductance of a Solenoid

Physics β†’ Electromagnetism β†’ Induction β†’ Inductors
$$L = \frac{\mu_0 N^2 A}{l}$$
Calculates the inductance of a long solenoid.
πŸ“– Physics πŸ“š Induction

Coulomb's Constant Formula

Physics β†’ Electromagnetism β†’ Electrostatics β†’ Constants
$$k_e = \frac{1}{4\pi\epsilon_0}$$
Relates the SI units of charge to the electrostatic force.
πŸ“– Physics πŸ“š Electrostatics

Kinetic Energy of Rotation

Physics β†’ Mechanics β†’ Rotational Motion β†’ Energy
$$K_{rot} = \frac{1}{2}I\omega^2$$
Energy of a rigid body due to its rotation about an axis.
πŸ“– Physics πŸ“š Rotational Motion

Heat Capacity Formula

Physics β†’ Thermodynamics β†’ Calorimetry β†’ Specific Heat
$$Q = mc\Delta T$$
Calculates the amount of heat energy required to change the temperature of a substance.
πŸ“– Physics πŸ“š Calorimetry

Ampere's Circuital Law

Physics β†’ Electromagnetism β†’ Magnetism β†’ Magnetic Fields
$$\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}}$$
Relates the integrated magnetic field around a closed loop to the electric current passing through the loop.
πŸ“– Physics πŸ“š Magnetism

Kinetic Energy of a Photoelectron

Physics β†’ Modern Physics β†’ Photoelectric Effect β†’ Stopping Potential
$$eV_s = hf - \Phi$$
Relates stopping potential to the incident photon frequency and work function.
πŸ“– Physics πŸ“š Photoelectric Effect

Bragg's Equation

Physics β†’ Solid State β†’ Crystallography β†’ Diffraction
$$n\lambda = 2d \sin \theta$$
Explains why cleavage faces of crystals appear to reflect X-ray beams at certain angles.
πŸ“– Physics πŸ“š Crystallography

Magnetic Flux

Physics β†’ Electromagnetism β†’ Induction β†’ Flux
$$\Phi_B = BA \cos \theta$$
A measure of the total magnetic field passing through a given surface area.
πŸ“– Physics πŸ“š Induction
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