The dimension of 12ϵoE2 permittivity of free space and E:Intensity of electric field) is
Explanation
Force=PxVyTz
[MLT−2]=[MLT−2L−2]x[LT−1]y[T]z
Comparing the dimensions on both side, we get,
x=1, y=2, z=2
So, Force=[P1V2T2]
Pressure(P)=ForceArea . . . . . (1)
Since, Force=Mass×Acceleration
And, Acceleration=VelocityTime=[LT−1][T]=[LT−2]
∴ The dimensional formula of force =[M][LT−2]=[MLT−2] . . . . (2)
The dimensional formula of area is [M0L2T0] . . . . (3)
On substituting equation (2) and (3) in equation (1) we get,
Pressure(P)=ForceArea
Or,
P=[MLT−2][L2]=ML−1T−2
Therefore, the pressure is dimensionally represented as [ML−1T−2]
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