The dimension of $1 half straight epsilon subscript straight o straight E squared comma space where space straight epsilon subscript straight o$ , is permittivity of free space and E is electric field is

[ML²T^-2]

[ML^-1T^-3]

[ML²T^-1]

[MLT^-2]

Solution

[ML^-1T^-3]

Dimensions space of space straight epsilon subscript straight o space equals space left square bracket space straight M to the power of negative 1 end exponent straight L to the power of negative 3 end exponent straight T to the power of 4 straight A squared right square bracket Dimensions space of space straight E space equals space left square bracket MLT to the power of negative 3 end exponent space straight A to the power of negative 1 end exponent right square bracket Therefore comma space Dimensions space of space 1 half straight epsilon subscript straight o straight E squared space equals space left square bracket straight M to the power of negative 1 end exponent straight L to the power of negative 3 end exponent straight T to the power of 4 straight A squared right square bracket space straight x space left square bracket straight M squared straight L squared straight T to the power of negative 6 end exponent straight A to the power of negative 2 end exponent right square bracket equals space left square bracket ML to the power of negative 1 end exponent straight T to the power of negative 3 end exponent right square bracket

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