Knowing More on Unit of Electric Flux

Electric flux is the measure of an electric field or it is the method of describing the electric field strength at a specific distance from the causative charge of the field. It can also be thought of as the number of electric field lines intersecting at a given area. These field lines originate on the positive charge and end on the negative charge. Moreover, the electric field lines directed on a closed surface will be negative. Similarly, if the field lines are directed away from the closed surface, it will be positive. If every field line directed into the surface continues from the interior and directs towards the outward someplace else than the surface, there will be no net charge within the closed surface. As the magnitude of positive electric flux is equal to the negative electric flux, the net electric flux will be zero. The famous Gauss’s law shows the mathematical relation between electric flux and enclosed charge. 

Unit of Electric Flux

The electric flux, being a scalar quantity, only has magnitude but no direction, and the unit of electric flux is Nm2/C (Newton-meters squares per coulomb).

Electric Flux

The electric flux will be the rate of flow of the electric field of any given area and is also proportional to the electric field lines.

Electric Flux for a Uniform Electric Field

If the given electric field is uniform, then the electric flux passing through the surface will be: 

ΦE = E.S. cosθ 

Here, 

ΦE = Electric Flux

E= The magnitude of the given electric field

S= Surface area 

θ= The angle formed between the electric field lines and the normal to S.

Electric Flux for a Non-Uniform Electric Field

For a given non-uniform field, the formula for the electric flux through a small surface area is as follows:

ΦE= surfaceE⋅dS 

Here, E= The magnitude of the given electric field

dS= Surface area 

Electric Flux and the Gauss’s Law

The formula according to Gauss’s Law describing the electric flux over a surface S is given as:

ΦE=∫E⋅dS 

Here, 

E= Electric Field

dS= Differential area of the given surface S.

Note: Electric flux is not affected by the charges outside the closed surface. However, the net electric field, E of the Gauss’ Law equation shall get affected due to the charges lying outside the closed surface. Gauss’s Law is applicable for all situations. However, it is only applicable for the ‘by hand’ calculations. 

Gauss’s Law

Gauss’s Law (one of the four important equations of Maxwell’s on electromagnetism) states that the total electric flux of any electric field within a closed surface is directly proportional to its enclosed electric charges. Carl Friedrich Gauss was the scientist who first introduced this law in 1835. However, this law was released as a part of a collection of work by the scientist in 1867. Moreover, it states that the electric flux is the product of an electric field passing through a given area and the area of the surface perpendicular to the given field. Moreover, the quotient obtained by dividing the total electric flux of any electric field by the enclosed charge will be equal to a constant value. The given positive electric charges might tend to generate a positive electric field. 

Solved Questions on Electric Flux 

Q 1 – Determine the electric flux of a uniform electric field with a magnitude of 400 N/C incidents on a plane surface. The surface area of this plane is 10m2 and the angle subtended by it is 30 degrees. 

Solution:

Using the formula of the electric flux for a uniform electric field:

ΦE= E.S. cosθ 

ΦE= 400× 10× cos30∘

ΦE =2003 Nm2/C. 

Answer: The electric flux of a uniform electric field with a magnitude of 400 N/C incidents on a plane surface is 2003 Nm2/C. 

Q 2 – What will be the magnitude of an electric flux of an electric field of 6 N/C? This electric field is in the Z-direction through a rectangle. The surface area of a rectangle is 6m2 in the given xy-plane. 

Solution: 

For the calculation of the electric flux, firstly we must determine the magnitude of the electric field, the angle between E and the normal vector and the area of some surface. 

According to the data given in the question:

E= 6k N/C

A= 6m2

Area=?

As given in the question, the direction of the electric field is in the z-direction. However, we do not know about the direction of the normal vector. Therefore, we can assume it is up direction. According to the formula of the electric flux for a uniform electric field:

ΦE= E.S. cosθ 

ΦE= 6× 6× cos0∘

ΦE =36 Nm2/C. 

Answer: The magnitude of an electric flux of an electric field of 4 N/C in the Z-direction through a rectangle is 36 Nm2/C. 

Conclusion

Electric flux is the measure of the electric field in electromagnetism within a given surface. Electric flux can also be referred to as the number of electric field lines intersecting at a given area. The electric flux is a scalar quantity (having magnitude but no direction) and the unit of electric flux is newton-meters squared per coulomb (N · m2 /C). If the given electric field is uniform, the electric flux passing through the surface will be ΦE=E⋅S=E.S. cosθ. On the other hand, for a given non-uniform field, the formula for the electric flux through a small surface area will be: dΦE= E⋅dS.