Physics Equations and Constants

Physics Equations and Constants

Uniform Electric Fields and Electric Potential

• Electric Force: $F<em>e = k</em>e \frac{q<em>1 q</em>2}{r^2}$
  • Where:
    • $F_e$ is the electric force.
    • $k_e = 9.00 \times 10^9 \frac{N \cdot m^2}{C^2}$ is Coulomb's constant.
    • $q<em>1$ and $q</em>2$ are the magnitudes of the charges.
    • $r$ is the distance between the charges.
• Electric Potential: $V = \frac{k_e q}{r}$
  • Where:
    • $V$ is the electric potential.
    • $k_e = 9.00 \times 10^9 \frac{N \cdot m^2}{C^2}$ is Coulomb's constant.
    • $q$ is the magnitude of the charge.
    • $r$ is the distance from the charge.
• Electric Field: $E = \frac{F}{q}$
• Change in Electric Potential: $\Delta V = Ed$
  • Where:
    • $\Delta V$ is the change in electric potential.
    • $E$ is the electric field.
    • $d$ is the distance over which the potential changes.
• Work Done: $W = q \Delta V$
  • Where:
    • $W$ is the work done.
    • $q$ is the charge.
    • $\Delta V$ is the change in electric potential.

Circuits

• Current: $I = \frac{\Delta Q}{\Delta t}$
  • Where:
    • $I$ is the current.
    • $\Delta Q$ is the change in charge.
    • $\Delta t$ is the change in time.
• Ohm's Law: $V = IR$
  • Where:
    • $V$ is the voltage.
    • $I$ is the current.
    • $R$ is the resistance.
• Power: $P = IV$
  • Where:
    • $P$ is the power.
    • $I$ is the current.
    • $V$ is the voltage.
• Power (alternative form): $E = Pt$
• Energy consumed: $1 kWh = 3.6 \times 10^6 J$
• Resistance: $R = \rho \frac{L}{A}$
  • Where:
    • $R$ is the resistance.
    • $\rho$ is the resistivity.
    • $L$ is the length.
    • $A$ is the cross-sectional area.
• Equivalent Resistance (series): $R<em>{eq} = R</em>1 + R<em>2 + … + R</em>n$
  • Where:
    • $R_{eq}$ is the equivalent resistance.
    • $R<em>1$, $R</em>2$, …, $R_n$ are the individual resistances.
• Equivalent Resistance (parallel): $\frac{1}{R<em>{eq}} = \frac{1}{R</em>1} + \frac{1}{R<em>2} + … + \frac{1}{R</em>n}$
  • Where:
    • $R_{eq}$ is the equivalent resistance.
    • $R<em>1$, $R</em>2$, …, $R_n$ are the individual resistances.

Magnets

• Magnetic Force on a Moving Charge: $F = qvBsin\theta$

  • Where:
    • $F$ is the magnetic force.
    • $q$ is the charge.
    • $v$ is the velocity.
    • $B$ is the magnetic field strength.
    • $\theta$ is the angle between the velocity and the magnetic field.

• Magnetic Force on a Current-Carrying Wire: $F = BILsin\theta$

  • Where:
    • $F$ is the magnetic force.
    • $B$ is the magnetic field strength.
    • $I$ is the current.
    • $L$ is the length of the wire.
    • $\theta$ is the angle between the current and the magnetic field.

• Magnetic Flux: $B = BAcos\theta$

• Induced Voltage: $V = -N \frac{\Delta \phi}{\Delta t}$
  *Where:
  * $V$ is the induced voltage.
  * $N$ is the number of turns in the coil.
  * $\phi$ is the magnetic flux.

• Radius of Circular Path in Magnetic Field: $r = \frac{mv}{qB}$

  • Where:
    • $r$ is the radius.
    • $m$ is the mass.
    • $v$ is the velocity.
    • $q$ is the charge.
    • $B$ is the magnetic field strength.

• Period of Circular Motion in Magnetic Field: $T = \frac{2\pi m}{qB}$

  • Where:
    • $T$ is the period.
    • $m$ is the mass.
    • $q$ is the charge.
    • $B$ is the magnetic field strength.

Sound

• Wave Velocity: $v = \lambda f$
  • Where:
    • $v$ is the velocity.
    • $\lambda$ is the wavelength.
    • $f$ is the frequency.
• Period and Frequency: $T = \frac{1}{f}$
  • Where:
    • $T$ is the period.
    • $f$ is the frequency.
• Speed of sound: $V_{sound} = 343 m/s$
• Doppler Effect: $f<em>o = f</em>s \frac{(v - v<em>o)}{(v - v</em>s)}$
  • Where:
    • $f_o$ is the observed frequency.
    • $f_s$ is the source frequency.
    • $v$ is the speed of sound.
    • $v_o$ is the velocity of the observer.
    • $v_s$ is the velocity of the source.
• Wavelength in a tube open at both ends: $\lambda_n = \frac{2L}{n}$
• Frequency in a tube open at both ends: $f_n = n\frac{v}{2L}$
• Frequency in a tube open at one end: $f_n = n\frac{v}{4L}$

Light

• Wave Velocity: $c = \lambda f$
  • Where:
    • $c$ is the speed of light.
    • $\lambda$ is the wavelength.
    • $f$ is the frequency.
• Speed of light: $c = 3.00 \times 10^8 m/s$
• Index of Refraction: $n = \frac{c}{v}$
  • Where:
    • $n$ is the index of refraction.
    • $c$ is the speed of light in a vacuum.
    • $v$ is the speed of light in the medium.
• Snell's Law: $n<em>1sin\theta</em>1 = n<em>2sin\theta</em>2$
  • Where:
    • $n<em>1$ and $n</em>2$ are the indices of refraction of the two media.
    • $\theta<em>1$ and $\theta</em>2$ are the angles of incidence and refraction, respectively.
• Magnification: $M = \frac{h<em>i}{h</em>o} = -\frac{d<em>i}{d</em>o}$
  • Where:
    • $M$ is the magnification.
    • $h_i$ is the image height.
    • $h_o$ is the object height.
    • $d_i$ is the image distance.
    • $d_o$ is the object distance.

Constants

• Elementary charge: $e = \pm 1.60 \times 10^{-19} C$
• Mass of electron: $m_e = 9.11 \times 10^{-31} kg$
• Mass of proton: $m_p = 1.67 \times 10^{-27} kg$