Dimension of Electric Flux: Learn to Derive

Find out how you can derive the dimension of electric flux using formulas of electric field and flux. And also know how the same electric flux dimensional formula gives us two SI units. 

To solve electrostatics problems correctly in Class 12 Physics and do great in your exams, it’s ideal to be clear with the dimension of electric flux. Not a superficial familiarity, though!

The meaning of flux in physics is better understood if you recall how electric flux describes the number of field lines intersecting across a geometric surface. It’s a scalar quantity, being a dot product of electric field and area vectors. 

Don’t simply rote learn the formulas. What gives you a more rewarding learning experience is figuring out the electric flux unit and dimension. With that, you can be way more confident in using the base quantities of mass, length, time, and current and approach Gauss’ Law numerical problems better in your boards and competitive exams. 

Formulas You Should Know for Deriving the Dimension of Flux 

Before going ahead with the dimension of flux, begin by dissecting the formulas of the electric field and flux you learnt in (or can go back to) Class 12th Physics Chapter 1 notes. 

Formula of Electric Field

The basic mathematical expression of the electric field comes from Coulomb’s Law, where we learn that a point charge creates an electric field at a distance.

E = kq/r^2

E is the electric field symbol, k is the Coulomb Constant, q is the charge, and r is the distance. 

We can also use this expression to define the force on a test charge, using a simpler formula that defines how much force there is per unit charge at any point. 

E = F / q

Here, the electrostatic force from Coulomb’s Law comes from substituting the F = k x q_1q_2/ r^2. Also, we do not need to use k (k = 1/4πε_0) here as it is a constant and does not really affect the dimension of the physical quantity. 

Formulas of Electric Flux 

In a uniform electric field, we have the electric flux formula as,

ΦE = E x A 

E is the electric field intensity, and a vector quantity

A is the surface area, and also a vector 

And, when the surface is non-uniform and the orientation of the electric field is slightly tilted, we have 

ΦE = E x A x cosθ 

θ is the angle between E and the normal to the surface.

Electric Flux Dimensional Formula with Derivation

To begin with electric flux dimension derivation, follow these steps. 

• Use the above equation, ΦE = E x A. 
• Electric Field E is known as E = F/q
• It's simpler after this. For Force, we have F = [M¹L¹T⁻²] and Charge, q = [I¹T¹] 
• Then we multiply both, we have E = [M¹L¹T⁻³I⁻¹]
• We then move to the Area or A, which is, [L²]
• After that, we multiply the two as [M¹L¹T⁻³I⁻¹] x [L²] 

So, the dimension formula of electric flux is

ΦE = [M¹L³T⁻³I⁻¹]

Now this simple-to-derive flux dimensional formula helps you with a lot more. You can check for errors in the MCQs and even compare with similar physical quantities like the dimension of magnetic flux, which is ΦB = [M¹L²T⁻²A⁻¹]. 

SI Unit and Interpretation of Electric Flux

You will find two SI units of electric flux, unlike a single SI Unit of electric charge.
One is Volt metre, with the short form V m. The other one is Newton metre squared per Coulomb, abbreviated from N m²/C. 

Why two?
The electric flux unit and dimension for both are identical and give you the same result, [M¹L³T⁻³I⁻¹].