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The dimension of ((1)/(2))epsilon(0)E^(2...

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

A

`MLT^(-1)`

B

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

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
Here , `(1//2) epsilon_(0) E_(2)` represents energy per unit volume .
`|epsilon_(0)| [E^(2)] = ("Energy")/("Volume") = ([ML^(2)T^(-2)])/([L^(3)]) = ML^(-1)T^(-2)`
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Knowledge Check

  • The dimensions of 1/2 epsilon_(0)E^(2) (epsilon_(0)= permittivity of free space, E= electric field) is

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

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

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

  • 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)]`