Question

# Prove that $1debye={{10}^{-18}}^{}esu$ $cm=3.335×{10}^{-30}Cm$

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Solution

## Step 1:Given,Static coulomb is the physical unit of electric charge used in the esu - CGS unit.$1staticcoulomb/esu=3.335×{10}^{-10}C.$Dipole moment of a system is defined as the product of charge and distance of separation between the charges.Debye is defined as the dipole moment resulting from a dipole having a charge of 10-10 esu separated by a distance of$1angstrom={10}^{-8}cm$.Step 2 Formula used,$Dipolemoment=charge×dis\mathrm{tan}ceofseperation$Step 3: SolutionCalculation of 1 debye in esu cm$Dipolemomentindebye={10}^{-10}esu×1angstrom\phantom{\rule{0ex}{0ex}}1debye={10}^{-10}esu×{10}^{-8}cm\phantom{\rule{0ex}{0ex}}={10}^{-18}esucm$Calculation of 1 debye in C m. $1debye={10}^{-18}esucm\phantom{\rule{0ex}{0ex}}1esu=3.335×{10}^{-10}C\phantom{\rule{0ex}{0ex}}1cm={10}^{-2}m\phantom{\rule{0ex}{0ex}}So,\phantom{\rule{0ex}{0ex}}1debye={10}^{-18}×3.335×{10}^{-10}C×{10}^{-2}m\phantom{\rule{0ex}{0ex}}=3.335×{10}^{-30}Cm$ Hence , 1 debye = 10-18 esu cm = 3.335× 10-30 C m is proved.

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