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α (θ_{i}, n_{1}, n_{2})

$alpha(theta_i, n_1, n_2)$ for EM waves

Last modified by TylerJones on Jul 24, 2020, 6:28:07 PM

This equation calculates $α$ $alpha$ (using $θ_{i}$ $theta_i$ , $n_{1}$ $n_1$ , and $n_{2}$ $n_2$ ), used in calculating the amplitudes of EM waves striking an interface. For more information and context on this equation, please see the EM waves at the interface of two insulators.

α (θ_{i}, θ_{t})

$alpha(theta_i, theta_t)$ for EM waves

Last modified by TylerJones on Jul 24, 2020, 6:28:07 PM

This equation calculates $α$ $alpha$ (using $θ_{i}$ $theta_i$ and $θ_{t}$ $theta_t$ ), used in calculating the amplitudes of EM waves striking an interface. For more information and context on this equation, please see the EM waves at the interface of two insulators.

β (μ_{1}, μ_{2}, n_{1}, n_{2})

$beta(mu_1, mu_2, n_1, n_2)$ for EM waves (in an insulator)

Last modified by TylerJones on Jul 24, 2020, 6:28:07 PM

This equation calculates $α$ $alpha$ (using $μ_{1}$ $mu_1$ , $μ_{2}$ $mu_2$ , $n_{1}$ $n_1$ , and $n_{2}$ $n_2$ ), used in calculating the amplitudes of EM waves striking an interface. For more information and context on this equation, please see the EM waves at the interface of two insulators.

β (μ_{1}, μ_{2}, v_{1}, v_{2})

$beta(mu_1, mu_2, v_1, v_2)$ for EM waves (in an insulator)

Last modified by TylerJones on Jul 24, 2020, 6:28:07 PM

This equation calculates $α$ $alpha$ (using $μ_{1}$ $mu_1$ , $μ_{2}$ $mu_2$ , $v_{1}$ $v_1$ , and $v_{2}$ $v_2$ ), used in calculating the amplitudes of EM waves striking an interface. For more information and context on this equation, please see the EM waves at the interface of two insulators.

d

$d$ (attenuating EM wave)

Last modified by TylerJones on Jul 24, 2020, 6:28:07 PM

This equation describes the "skin depth"¹ ( $d$ $d$ ) of an electromagnetic wave in a conducting medium. The "skin depth" is how far the wave can travel before the amplitude of its electric field is reduced by a factor of $\frac{1}{e}$ $1/e$

^ Griffiths, David J. "Electromagnetic Waves in Matter." Introduction to Electrodynamics. 4th ed. N.p.: Prentice Hall, 2013. 413. Print.

k

$k$ (attenuating EM wave)

Last modified by TylerJones on Jul 24, 2020, 6:28:07 PM

This equation describes the real portion ( $k$ $k$ ) of the complex wavenumber¹ ( $\tilde{k}$ $tilde k$ ) of an electromagnetic wave in a conducting medium. $k$ $k$ is a spatial angular frequency, normally given the units of rad/m. vCalc doesn't currently have any other unit options for angular spatial frequency, but feel free to request them using the "contact us" button at the bottom.

^ Griffiths, David J. "Electromagnetic Waves in Matter." Introduction to Electrodynamics. 4th ed. N.p.: Prentice Hall, 2013. 413. Print.

κ

$kappa$ (attenuating EM wave)

Last modified by TylerJones on Jul 24, 2020, 6:28:07 PM

This equation describes the imaginary portion ( $κ$ $kappa$ ) of the complex wavenumber¹ ( $\tilde{k}$ $tilde k$ ) of an electromagnetic wave in a conducting medium. $κ$ $kappa$ is a spatial angular frequency, normally given the units of rad/m. vCalc doesn't currently have any other unit options for angular spatial frequency, but feel free to request them using the "contact us" button at the bottom.

^ Griffiths, David J. "Electromagnetic Waves in Matter." Introduction to Electrodynamics. 4th ed. N.p.: Prentice Hall, 2013. 413. Print.

{\tilde{E}}_{0_{R_{∣ ∣}}}

$tilde E_(0_(R_(||)))$ at the interface of insulators

Last modified by TylerJones on Jul 24, 2020, 6:28:07 PM

This equations solves for the parallel component of the reflected amplitude at an interface of insulating media.

{\tilde{E}}_{0_{R_{⊥}}}

$tilde E_(0_(R_bot))$ at the interface of insulators

Last modified by TylerJones on Jul 24, 2020, 6:28:07 PM

This equations solves for the perpendicular component of the reflected amplitude at an interface of insulating media.

{\tilde{E}}_{0_{T_{∣ ∣}}}

$tilde E_(0_(T_(||)))$ at the interface of insulators

Last modified by TylerJones on Jul 24, 2020, 6:28:07 PM

This equations solves for the parallel component of the transmitted amplitude at an interface of insulating media.

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