Question 286: Units , Dimensions and Error Analysis

Question

The dimension of $\left( {{1 \over 2}} \right){\varepsilon _0}{E^2}$
( ${\varepsilon _0}$ : permittivity of free space, E electric field )

Accepted Answer

Dimension of $\varepsilon $
0
= M
$-$1
L
$-$3
T
4
A
2
Dimension of electric field E = MLT
$-$3
A
$-$1
Now, dimension of
${1 \over 2}$$\varepsilon $
0
E
2
= (M
$-$1
L
$-$3
T
4
A
2
)(MLT
$-$3
A
$-$1
)
2
= M
$-$1
L
$-$3
T
4
A
2
M
2
L
2
T
$-$6
A
$-$2
= ML
$-$1
T
$-$2
Answer (C)

Answer

MLT
-1

Answer

ML
2
T
-2

Answer

ML
-1
T
-2

Answer

ML
2
T
-1

Units , Dimensions and Error Analysis

The dimension of \left( {{1 \over 2}} \right){\varepsilon _0}{E^2} ( {\varepsilon _0} : permittivity of free space, E electric field )

Choose the correct answer: