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Find the dimensional formula of (1)/(4 p...

Find the dimensional formula of `(1)/(4 pi "in"_0) (e^2)/(hc)`, where symbols have their usual menaing.

Text Solution

Verified by Experts

The correct Answer is:
`[M^0L^0T^0]`
`(e^2)/(4pi "in"_0hc) = (F r^2)/(hc), where F =(e^2)/(4pi "in"_0r^2)`
`=([MLT^(-2)][L^2])/([ML^2T^(-1)][LT^(-1)]) =1 = [M^0 L^0T^0]`
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Knowledge Check

  • What is the dimensional formula of (1)/(mu_(0)epsilon_(0)) where the symbols have their usual meanings?

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

  • Which of the following represents correct dimensional formula of 1/2 epsi_0 E^2 where symols have usual meanings ?

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

  • The dimensional formula of 1/(mu_0in_0) is ..........

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

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