Unit and dimensions of electric flux

Let the electric field at the position of surface element dA be E.

Hence,

The electric flux is mathematically defined as follows.

dΦₑ =→E.d→A

Electric flux with respect to the whole surface

or,

dΦₑ=∫ₐ→E.d→A

Φₑ= →E.→A

Φₑ=E.A.Cosθ

Φₑ=0

Case 1

When, θ= 0°

Φₑ=E.A.Cos0°

Φₑ=E.A

In this case the plane surface is normal to the electric field E.

Case 2

When,θ=90°

Φₑ=E.A.Cos90°

Φₑ=0

In this case the plane surface is parallel to the electric field E.

Unit and dimension of electric flux-

Φₑ=E.A

Φₑ=(Newton/Coulomb).meter²

Φₑ=Newton.Coulomb⁻¹.meter²

Φₑ=NC⁻¹M²

Dimensions

Φₑ=[MLT⁻²(AT)⁻¹L²]

Φₑ=[ML³T⁻³A⁻¹]