Question

The value of ${\epsilon }_0$ (permittivity of the free space) is

• A. $8.854\times {10}^{-12}\frac{coulomb}{N{m}^2}$
• B. $8.854\times {10}^{-12}\frac{N{m}^2}{coulom{b}^2}$
• C. $8.854\times {10}^{-12}\frac{coulom{b}^2}{N{m}^2}$
• D. $8.854\times {10}^{12}\frac{coulom{b}^2}{N{m}^2}$

Answer 1

The correct option is C $8.854\times {10}^{-12}\frac{coulom{b}^2}{N{m}^2}$

From $F=\frac{1}{4\pi {\epsilon }_o}\frac{q^2}{r^2}$

If Force, $F=1N$

charge, $q=1C$

distance, $r=1m$

Then, $q_o=\frac{q^2}{F\times 4\pi \times r^2}$

$=\frac{(1{)}^2}{1N\times 4\times 3.14\times (1m{)}^2}$

${\epsilon }_o=8.854\times {10}^{-12}\frac{C^2}{N{m}^2}$