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Obtain the dimensional formula for varep...

Obtain the dimensional formula for `varepsilon_(0)`.

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`F=1/(4pivarepsilon_(0))(q_(1)q_(2))/r^(2)implies" "varepsilon_(0)=1/(4pi)(q_(1)q_(2))/(Fr^(2))`. Therefore, `[ɛ_(0)] = 1/(4pi)([q_(1)][q_(2)])/([F][r^(2)])`
Here, `1/(4pi)` is dimensionless and `[q_(1)] = [AT], [q_(2)] = [AT], [F] = [MLT^(-2)], [r^(2)] = [L^(2)]`
Hence, `" "[varepsilon_(0)]=([AT][AT])/([MLT^(-2)][L^(2)]` or `[varepsilon_(0)]` = `[M^(-1)L^(-3)T^(4)A^(2)]`
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Knowledge Check

  • The dimensional formula of stress is

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

  • The dimensional formula of stress is

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

  • The dimensional formula of torque is

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

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