Encyclopedia Magnetica™

Conversion from the CGS to SI format

Go back to: Calculator of inductance of a pair of parallel round straight wires

These CGS to SI conversions were carried out by Stan Zurek.

Equation 1)

From [1] Grover, eq. (19), p. 40, (two wires with arbitrary diameters)

L = 0.002 * l * { log_e [ d^2 / (rho1 * rho2) ] + 1/2 }

d = s (wire spacing), rho1 = d1/2, rho2 = d2/2 (wire radii rho and diameters d), 
and log_e represents the natural logarithm

L = 0.002 * l * { log_e [ s^2 / ( d1/2 * d1/2 ) ] + 1/2 }

L = 0.002 * l * { log_e [ s^2 / (d1 * d1 / 4 ) ] + 1/2 }

L = 0.002 * l * { log_e [ 4 * s^2 / (d1 * d1)]  + 1/2 }

if l is in (cm) then the Grover's factor 0.002 has the units of (uH/cm), 
but u0 has the units of (H/m), hence

0.002 (uH/cm) = 0.002 * 1e-6 / 1e-2 (H/m) = 2e-3 * 1e-4 (H/m) = 2e-7 (H/m)

and since: u0 = 4 * pi * 1e-7 (H/m)

then Grover's 0.002 factor is:

0.002 uH/cm = u0 / (2 * pi) in (H/m)

so the final equation with all variables in base SI units is:

L_SI = u0 * l /(2*pi) * { log_e [ 4 * s^2 / (d1 * d1) ] + 1/2 }

Equation 2)

From [1] Grover, eq. (16), p. 39, (two wires with the same diameter)

L = 0.004 * l * { log_e ( d / rho ) + 1/4 - d/l }

d = s (wire spacing), rho = d1 (wire radius rho and diameter d1), 
and log_e represents the natural logarithm

L = 0.004 * l * { log_e [ s / ( d1 /2 ) ] + 1/4 - s/l }

L = 0.004 * l * [ log_e ( 2 * s / d1 ) + 1/4 - s/l ]

if l is in (cm) then the Grover's factor 0.004 has the units of (uH/cm), 
but u0 has the units of (H/m), hence

0.004 (uH/cm) = 0.004 * 1e-6 / 1e-2 (H/m) = 4e-3 * 1e-4 (H/m) = 4e-7 (H/m)

and since: u0 = 4 * pi * 1e-7 (H/m)

then Grover's 0.004 factor is:

0.004 uH/cm = u0 / pi in (H/m)

so the final equation with all variables in base SI units is:

L_SI = u0 * l / pi * [ log_e ( 2 * s / d1 ) + 1/4 - s/l ]

Equation 3)

Eq. (3) is from [2] Paul, eq. (7.4), p. 316, (two wires with the same diameter), which is already given in the SI format.

Equation 4)

From [2] Grover, eq. (7), p. 35, single straight wire (no return, for comparison only)

L = 0.002 * l * [ log_e (2 * l / rho) - 3/4 ]

rho = d1/2 (wire radius rho and diameter d1), 
and log_e represents the natural logarithm

L = 0.002 * l * { log_e [2 * l / (d1 /2)] - 3/4 }

L = 0.002 * l * [ log_e ( 4 * l / d1 ) - 3/4 ]

if l is in (cm) then the Grover's factor 0.002 has the units of (uH/cm), 
but u0 has the units of (H/m), hence

0.002 (uH/cm) = 0.002 * 1e-6 / 1e-2 (H/m) = 2e-3 * 1e-4 (H/m) = 2e-7 (H/m)

and since: u0 = 4 * pi * 1e-7 (H/m)

then Grover's 0.002 factor is:

0.002 uH/cm = u0 / (2 * pi) in (H/m)

so the final equation with all variables in base SI units is:

L_SI = u0 * l / (2 * pi)  * [ log_e ( 4 * l / d1 ) - 3/4 ]

Derivations