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: