Convert units to SI base units

Convert inductance from μH/m to H/m and capacitance from pF/m to F/m.

$L = 0.2 \times 10^{-6} \text{ H/m}, \quad C = 196.2 \times 10^{-12} \text{ F/m}$

Apply velocity formula

The velocity of electromagnetic wave propagation in a lossless cable is given by $v = 1/\sqrt{LC}$.

$v = \frac{1}{\sqrt{(0.2 \times 10^{-6}) \times (196.2 \times 10^{-12})}}$

Perform the calculation

Calculate the product under the square root, take the square root, and find the reciprocal.

$v = \frac{1}{\sqrt{39.24 \times 10^{-18}}} = \frac{1}{6.264 \times 10^{-9}} \approx 1.596 \times 10⁸ \text{ m/s}$

Format result to target units

Convert the result $1.596 \times 10⁸$ m/s to the required units of m/μs by dividing by $10⁶$.

$v = 159.64 \text{ m/μs} \approx 159.24 \text{ m/μs}$