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Conversion of electromagnetic equations: CGS to MKS units

MKS to CGS

Tips and instructions for units conversion

Examples

As written Sage Cell (line 4)
$\nabla \times \vec{B} = \frac{1}{c}\frac{\partial \vec{E}}{\partial t}+\frac{4\pi}{c}\vec{J}$ eqCGS = B == c^(-1)*E + 4*pi*c^(-1)*J
$\vec{D}_1=\vec{E}_1+\vec{P}_1$ eqCGS = D == E + P
$\vec{F}=m\vec{a}$ eqCGS = f == m_ * a
$\frac{1}{\sqrt{4\mu_0 \pi}}$ (1/2)*mu_0^(-1/2)*pi^(-1/2)
$\vec{F}=q(\vec{E}+\frac{\vec{v}}{c}\times\vec{B})$ eqCGS= f == q*(E + v*c^(-1)*B)

Using the constant multiplier

The code enables you to multiply the entire equation by an overall factor. Here's an example to show how it works. In the "CGS to MKS" code box, on line 4 enter eqCGS = H-D/c==4*pi*J/c.
On line 6, enter eq = eqCGS * 1 (corresponding to a multiplier of 1), and press Evaluate.
In the answer box, you will see: $-2D\sqrt{\mu_0} \sqrt{\pi} + 2H\sqrt{\mu_0} \sqrt{\pi} = 2J\sqrt{\mu_0} \sqrt{\pi}$.
Now change the overall multiplicative factor $1/\sqrt{4 \mu_0 \pi}$ on line 6: eq = eqCGS * (1/2)*mu_0^(-1/2)*pi^(-1/2), and press Evaluate.
You should now see the simpler equation: $-D+H=J$

Electromagnetic Variables

Quantity Gaussian SI Sage Cell
Mass $m$ $m$ m_,M_
Lenth $l$ $l$ l
Time $t$ $t$ t
Force $\vec{F}$ $\vec{F}$ f, F_
Energy $W$ $W$ W
Energy density $w$ $w$ w
Power $P$ $P$ Pow, P_
Power flow density $\vec{S}$ $\vec{S}$ S
Charge $q$ $\frac{q}{\sqrt{4 \pi \epsilon_0}}$ q
Surface charge density $\sigma, \Sigma$ $\frac{(\sigma, \Sigma)}{\sqrt{4 \pi \epsilon_0}}$ Sigma
Charge density $\rho$ $\frac{\rho}{\sqrt{4 \pi \epsilon_0}}$ rho
Current $I$ $\frac{I}{\sqrt{4 \pi \epsilon_0}}$ I
Current density $\vec{J}$ $\frac{\vec{J}}{\sqrt{4 \pi \epsilon_0}}$ J
Polarization $\vec{P}$ $\frac{\vec{P}}{\sqrt{4 \pi \epsilon_0}}$ P
Electric diple moment $\vec{p}$ $\frac{\vec{p}}{\sqrt{4 \pi \epsilon_0}}$ p
Electric field $\vec{E}$ $\sqrt{4 \pi \epsilon_0}\vec{E}$ E
Potential (Emf, Voltage) $\Phi, V$ $\sqrt{4 \pi \epsilon_0}(\Phi, V)$ Phi, V
D-field $\vec{D}$ $\sqrt{\frac{4 \pi}{\epsilon_0}}\vec{D}$ D
Magnetic field $\vec{B}$ $\sqrt{\frac{4 \pi}{\mu_0}}\vec{B}$ B
Vector potential $\vec{A}$ $\sqrt{\frac{4 \pi}{\mu_0}}\vec{A}$ A
H-field $\vec{H}$ $\sqrt{4 \pi \mu_0}\vec{H}$ H
Magnetization $\vec{M}$ $\sqrt{\frac{\mu_0}{4 \pi}}$ M
Magnetic moment $\vec{m}$ $\sqrt{\frac{\mu_0}{4 \pi}}\vec{m}$ m
Magnetic Flux $F_{ij}$ $\sqrt{\frac{4 \pi}{\mu_0}}F_{ij}$ F
Conductivity $\sigma$ $\frac{\sigma}{4 \pi \epsilon_0}$ sigma
Dielectric constant $\epsilon$ $\frac{\epsilon}{\epsilon_0}$ epsilon
Magnetic permeability $\mu$ $\frac{\mu}{\mu_0}$ mu
Resistance $R$ $4 \pi \epsilon_0 R$ R
Inductance $L$ $4 \pi \epsilon_0 L$ L
Capacitance $C$ $\frac{C}{4 \pi \epsilon_0}$ C