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The dimensions of (1)/(2) in(0) E^(2), w...

The dimensions of `(1)/(2) in_(0) E^(2)`, where `in_0` is permittivity of free space and E is electric field, is :-

A

`[ML^(2)T^(-2)]`

B

`[ML^(-1)T^(-2)]`

C

`[ML^(2)T^(-1)]`

D

`[MLT^(-1)]`

Text Solution

Verified by Experts

The correct Answer is:
B
Energy density of an electric field E is `u_(E)= (1)/(2)epsilon_(0)E^(2)`
Where `epsilon_(0)` is permittivity of free space
`mu_(E)= ("Energy")/("Volume")= ([ML^(2)T^(-2)])/([L^(3)])= [ML^(-1)T^(-2)]`
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Knowledge Check

  • Find the dimension of epsilon_(0)E^(2) , where epsilon_(0) is permittivity of free space and E is the electricity field

    A
    `[M^(1) L^(1) T^(-2) A^(1)]`
    B
    `[M^(1) L^(0)T^(-1)]`
    C
    `[M^(1) L^(-1) T^(-2) A^(1)]`
    D
    `[M^(1) L^(-1) T^(-2)]`

  • The dimension of ((1)/(2))epsilon_(0)E^(2) ( epsilon_(0) : permittivity of free space, E electric field

    A
    (a) `MLT^(-1)`
    B
    (b) `ML^(2)T^(2)`
    C
    ( c ) `ML^(-1)T^(-2)`
    D
    ( d ) `ML^(2)T^(-1)`

  • The dimensions of 1/2 in_(0) E^(2) ( in_(0) : permittivity of free space, E: electric field) is-

    A
    `[MLT^(-1)]`
    B
    `[ML^(2)T^(-2)]`
    C
    `[ML^(-1)T^(-2)]`
    D
    `[ML^(2)T^(-1)]`

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