## Introduction: Electric flux

Electrical flux is the measure of the electrical field through a given surface although an electrical field cannot flow in itself. It is a way to describe the strength of the electric field at any distance from the charge that causes the field.

At any point in space the electric field E will exert a force on an electrical charge. The electric field shall be proportional to the voltage gradient.

### Dimensional Formula of Electric Flux

The dimensional formula of electric flux is expressed by,

[M1 L3 T-3 I-1]

Where,

M = Mass

I = Current

L = Length

T = Time

Derivation

Electric Flux (ΦE) = E × S × cos θ -------------------------- (1)

Whereas,

E = Magnitude of the electric field

S = Surface Area

The dimensional formula of area (S) = [M0 L2 T0] --------------------------(2)

Since, Electric Field = [Force × Charge-1] . . . (3)

The Dimensional Formula of,

Force = m × a = [M1 L1 T-2] ------------------------(4)

Charge = current × time = [I1 T1] --------------------(5)

substitute equation (4) and (5) in to equation (3) the result obtained is ,

Electric Field = [M1 L1 T-2] × [I1 T1]-1

Therefore, The dimensional formula of Electric Field = [M1 L1 T-3 I-1] -------(6)

substitute equation (2) and (6) in equation (1) we observe,

⇒ Electric Flux = E × S × cos θ

Or, ΦE = [M1 L1 T-3 I-1] × [M0 L2 T0] = [M1 L3 T-3 I-1]

Thus, the electric flux is dimensionally shown as [M1 L3 T-3 I-1].

1. What is SI unit and Dimension of Electric Flux?

Ans. The dimensional formula of electric flux is represented by, [M^{1} L^{3} T^{-3} I^{-1}]

2. What is SI unit of Electric Flux?

Ans. Electrical flux has SI units of volt meters (V m), or, evenly, Newton meters squared per coulomb (N m^{2} C^{−1}). Thus, the SI base units of electric flux are kg·m^{3}·s^{−3}·A^{−1}.

3. Is Electric Flux a vector?

Ans. Flux is a vector quantity for transport phenomena, defining the magnitude and direction of flow of a material or property. Flux is a scalar quantity in vector calculus, defined as the integral surface of the perpendicular part of a vector field over a line.