Question

The dimension of `((1)/(2))epsilon_(0)E^(2)` (`epsilon_(0)` : permittivity of free space, E electric field
A. `[ML^(2)T^(-2)]`
B. `[ML^(-1)T^(-2)]`
C. `[ML^(2)T^(-1)]`
D. `[MLT^(-1)]`

Answer 1

Correct Answer - B
As we know that,
Dimension of `epsilon_(0) = [M^(-1)L^(-3)T^(4)A^(2)]`
Dimension of `E = [MLT^(-3)A^(-1)]`
So, dimension of
`(1)/(2) epsilon_(0)E^(2) = [M^(-1)L^(-3)T^(4)A^(2)] xx [MLT^(-3)A^(-1)]^(2)`
`=[ML^(-1)T^(-2)]`