Question

Find the dimensions of electric permittivity

• A. $[A^2{M}^{-1}{L}^{-3}{T}^4]$
• B. $[A^2{M}^{-1}{L}^3{T}^0]$
• C. $[A{M}^{-1}{L}^{-3}{T}^4]$
• D. $[A^2{M}^0{L}^{-3}{T}^4]$

Answer 1

Answer: (A)

From Coulombs law, the force of attraction/repulsion between two point charges q, q separated by distance $r$ is $F=\frac{1}{4\pi {\epsilon }_0}\frac{q^2}{r^2}$ $\Rightarrow$ ${\epsilon }_0=\frac{1}{4\pi }.\frac{q^2}{F{r}^2}$ where ${\epsilon }_0$ is electric permittivity. Dimensions of ${\epsilon }_0=\frac{{[AT]}^2}{[ML{T}^{-2}][L^2]}$ ${\epsilon }_0=[A^2{M}^{-1}{L}^{-3}{T}^4]$ Note: The constant ${\epsilon }_0$ (epsilon zero) is called permittivity of free space and its vaiue is $8.85\times {10}^{-12}$ $Couloum{b}^2/newtonmetr{e}^2$ .