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

The dimensions of `(1)/(2)epsilon_(0)E^(2)` `(epsilon_(0)=` permitivity of free space and `E`= electric field) are :

A

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

B

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

C

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

D

`[MLT^(-1)]`

Text Solution

Verified by Experts

The correct Answer is:
B
`(1)/(2)in_(0)E^(2)` is the expression for electrostatic energy density `i.e.` the energy stored per unit volume in a parallel plate capacitor.
`:.(1)/(2)in_(0)E^(2)represents=("Energy")/("Volume")`
`=(ML^(2)T^(-2))/(L^(3))=[ML^(-1)T^(-2)]`
Aliter.`epsilon_(0)=(1)/(4piF).(q_(1)q_(2))/(r^(2))` and `E=(F)/(q)`
`:.(1)/(2)epsilon_(0)E^(2)=(1)/(8piF)(q_(1)q_(2))/(r^(2))xx(F^(2))/(q^(2))=(F)/(r^(2))=(MLT^(-2))/(L^(2))`
`[ML^(-1)T^(-2)]`
Hence the correct choice is `(b)`.
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