NEET 2010
- Exam
- NEET
- Year
- 2010
- Subject
- Physics
- Chapter
- Units and Dimensions
NEET 2010 · Physics · Units and Dimensions
The dimension of (1)/(2) _0 E^2 , where _0 is permittivity of free...
The dimension of , where is permittivity of free space and is electric field, is
Options
- A
- B
- C
- D
Correct answer
B.
Step-by-step solution
\begin{aligned}
& \text{ Dimensions of } \varepsilon_0=\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^4 \mathrm{~A}^2\right] \\
& \text{ Dimensions of } \mathrm{E}=\left[\mathrm{MLT}^{-3} \mathrm{~A}^{-1}\right] \\
& \therefore \text{ Dimensions of } \frac{1}{2} \varepsilon_0 \mathrm{E}^2=\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^4 \mathrm{~A}^2\right] \\
& \quad=\left[\mathrm{ML}^{-1} \mathrm{~T}^{-3}\right] \quad \times\left[\mathrm{M}^2 \mathrm{~L}^2 \mathrm{~T}^{-6} \mathrm{~A}^{-2}\right]
\end{aligned}